You've got three questions here. I'll deal with them in order:
1) The term PoC (for "Person of Color"): I don't like any terms designed to designate race, particularly those who are descended from Africa, because the terms either don't make sense or are offensive to the people they are applied to.
"Negro": an old fashioned term, meaning "Black" in French. It is offensive to some people described this way.
"Black": as far as I can tell, this is less offensive to people described this way than any other term, making it my preference. However, if "black" is meant to approximate a fair description of skin color, it misses the mark for over 99% of the people I've met who would be described as "black". The darkest skin I've ever seen on a person was an Indian (from India). His skin could be mistaken for black. I've seen dozens of Indians whose skin color is so dark (no higher than 50 on a 256 point scale of luminance) that shadows are hidden by their skin color. I have seen photos of Africans that appear to have such dark skin but photos for publication are almost always manipulated, particularly contrast, so I prefer to trust my observations of people I've seen in person.
"N----": I won't spell this one out because it is so offensive that I won't speak it aloud or write it out. It is a corruption of "Negro", pronounced with a slur. Oddly, there is a subset of people who describe themselves this way without being offended. I'm offended by it, even when people use it to describe themselves.
"D----": Another offensive term, this one somewhat archaic, refers to "dark" skin. This is more accurate than "Black" and its variations because it is more likely that someone described this way will have darker skin than someone not described this way but that isn't always the case. My sister with a suntan is darker than many people who would be described like this. I've also met people whose skin is lighter than mine in the middle of winter who would be described like this, and those who I mistakenly believed were Caucasian.
"Colored": Read literally, this one is funny in a grammatical sense. Everyone has a color to start with, so a "colored" person would be someone who has been "colored" to change their color into something else. This clearly isn't the intended meaning but it is what I think of when I run across the word used to describe a person. The intended meaning is yet another reference to skin color but is inadequate in two ways. The first is that everyone has a color, so saying that someone is "colored" doesn't distinguish that person from anyone else. Second, the word "color" can be translated as "hue" and all humans have very similar hues in their skin. There is a range but it is extremely narrow. All human skin, barring those who have turned blue from ingesting silver, is a variation of orange. It is normally a low saturation orange, differentiated by luminosity, where some are lighter than others, depending on how close to the equator their ancestors lived. Some are a slightly yellower orange, others slightly more red, but neither are red or yellow. They remain orange but with a shift in either direction. I don't like this term because it is inexact, ungrammatical, and people described this way sometimes find it demeaning.
"Person of Color": This term, the one you used, has all the defects of "colored" in addition to sounding pretentious. It's like saying that the person is special or unique due to their connection or relationship to hue.
"African": No problem with this but there are Caucasian Africans descended from European settlers so it doesn't differentiate very well.
"African-American": This has the same problem as "African" and the additional problem that not all people described this way are African, American, or descended from either. They might be Jamaican, Aborigine, or even Swedish. This term doesn't bother me as most of the others because it isn't usually considered offensive by the people it is applied to and it does describe a large number of those it is applied to accurately. These days that may not be a majority, because it works best with people whose families have lived in America for over a hundred and fifty years and those who have immigrated to the US from Africa of their own will more recently.
There may be other terms but these are the ones that came to mind this morning. Of the lot, my preferred terms are, "black" and "African-American". Both are inaccurate but they seem to be accepted by the people they are applied to and there seems to be general agreement that they are not offensive. Despite this, I find constant references to race offensive. I prefer to think of people as people, just as Morgan Freeman said on this subject.
2) Your second question is whether I believe there is systemic or institutional racism in America or the American police force. My answer to both is "no". If I thought either was true, I wouldn't hesitate to denounce it. That said, I believe those claims are not only false but outright lies by people who should know better (and likely do). The lies are believed by their victims. They are victims of the lies because the lies persuade them to behave in a self-destructive and sometimes criminal manner. That in turn creates the potential for the lie to become true, by stimulating fear of one race and then pitting two or more races against each other. Your example of "where there is smoke, there is fire" is fitting but not in the way you might think. Sometimes, and these days it is increasingly the case, it is computer-generated. There are people who profit in various ways from racial strife. This was true in Booker T. Washington's day (which is why he complained about it) and it is true today. It does no one any good to perpetuate this myth and does considerable harm.
There is considerable research on the subject of systemic racism in the police force. Many of those studies return a conclusion that it is not so. More than that, it isn't even close. Some have found, if one can say there is an opposite to a thing like "racism" that the opposite is true. By a very large margin, for instance, white officers are far less likely to discharge a weapon against a black suspect than black police officers. Although suspects described as "unarmed black men" have been killed in police encounter, two critical items are often left out of those descriptions. The first is that the term "unarmed" appears to describe the suspect's state at the start of the encounter. If they become armed during the encounter, they are still described as "unarmed". For instance, in one recent case, an "unarmed suspect" grappled with a police officer, took his gun, and tried to shoot him with it. The police officer managed to get the better of the suspect and shot him. The second item, alluded to in the previous example, is that in at least half of these examples, the police officer is being attacked by the suspect at the time his weapon is discharged. In other words, they are clear examples of self-defense. My impression is that white officers are so terrified by the possibility they will be called "racist" if they shoot or injure a black suspect that they have ignored their police training to avoid that outcome. Some have died because they didn't defend themselves adequately for this reason.
It is also useful to be aware of how often this things happen and where they happen. If you look at the number of shootings involving a white police officer and a black suspect, they range between about 9-15 per year. Those numbers tend to about half the number of white police officers killed by black suspects. Both of those numbers are dwarfed by the number of black victims killed by black suspects and white victims killed by black suspects. Those higher numbers are dwarfed again by the number of police encounters overall, which is in the millions per year. Another factor often ignored by the media in discussions of this subject are the many black people who serve in government and the police force. There are cities that have a near black population majority (like Baltimore), a black mayor, black police commissioner, black police chief, and nearly 50% of the police force is black. There are examples of those departments in those cities being described as examples of "systemic racism" after one of the exceedingly rare examples of a white police officer shooting a black suspect occurs there.
Some say that all the evidence one needs of the racist American justice system is the number of black people incarcerated in American prisons. This can also be an indicator of who is committing the crimes. If they happen to be black more often than not, they will go to prison. Keep in mind that not all crimes are solved, not all criminals are caught, and not all criminals who are tried are convicted. The criminals who are caught and convicted represent a subset of the total number of criminals in the country at any given time. Whether the proportion caught and incarcerated represents their ratio by race of the total number of criminals cannot be known but the hurdles to incarceration are so high that even demonstrably guilty people are set free. This leads to the conclusion that most most of the people in prison are guilty of the crime they were convicted of. If this is true, then the system isn't racist because they are not favoring black incarceration over non-black incarceration. The preference is to incarcerate criminals over non-criminals, and that is as it should be.
Let's also be aware of the effect of black-on-black crime. Black suspects overwhelmingly prefer other black people as their victims. In some cases, this means one group of criminals committing crimes against another group of criminals. It also means black criminals destroying the lives of perfectly honest, hard-working black people, ravaging communities, making things much harder for other black people. This is why many black people want police in their communities. They have been known to beg for police to return to their communities. A syndrome you will find in America if you look is this: a black community is ravaged by crime. A white officer injures or kills a black suspect in a confrontation. Protests against the police erupt. The police voluntarily withdraw from the neighborhood, either to satisfy the demands, or out of caution for their own safety. After the police leave, crime gets worse than it was before. Members of the community beg for the police to return. They do, and crime goes down again, until the next time a cause is made of a police interaction and the cycle repeats.
My impression is that crime is a very bad thing, whether it is perpetrated by black people, white people, or space aliens. Crime is bad no matter who does it. That means I am against crime perpetrated by black criminals, whether the victims are black, white, or anything else. I am also against crime committed by Caucasians, Asians, and any other group you care to name (women, midgets, terriers, etc). Riots are crimes. Incitement to riot is a crime. Inducing a minor to commit a crime is a crime. In my opinion, the biggest criminals, the biggest racists in this entire mix are the media figures who encourage racism and criminal activity to "protest" the "racism" they invented and promote for their own reasons. I'd rather see major figures in entertainment accused of racism than see that accusation generically leveled against the police force in America because I think it actually describes entertainment and media figures much better than it does the police.
In the "fight against racism" we find almost all of the racists one could care to find. There likely are a few hard-core racists around, hiding in the shadows of society but they are marginalized figures with little to no influence. Racism as an ideology is frowned upon by a large consensus of Americans, including me. I have no respect for genuine racists, but the only ones I have seen these days are in the media. Getting back to the fight against racism, I see three groups: 1) promoters of racism. These people are racists themselves because they do make value judgments on the basis of race. The tendency is to equate white skin with moral inferiority or brutality. 2)Victims of promoters. These are people of all races who genuinely believe the racist lies broadcast by the promoters. I consider these people victims because they are harmed by their belief in the lies. At the lowest level of harm, they feel anger or sadness (or both) because of the lies. They are encouraged to engage in activities that disturb other's peace of mind. That also harms them because now they are victimizing others, which reduces their integrity, something they will regret when or if they ever learn the truth. Their protest activities, particularly when they turn violent, create fear in and around their community, perversely creating fear of "black people" because they have now been witnessed behaving irrationally and causing real harm to communities on that basis. Violent participants in riots, or victims who become so enraged by promoter's lies that they become criminals themselves, effectively destroy their own future, the lives of their family, and the lives and future of anyone they victimize, such as the many police officers wounded or killed by protester/rioters in the recent riots. 3) fearful members of all races, including black. These people do not believe the promoter's lies but they are afraid they will come to harm if they don't pretend to go along with them. For this reason, they will, for example, write "black-owned" on the front of their store to prevent it from being looted, or post a black square on Instagram to show fealty, not support, to a cause they don't believe in but don't want to be victimized by.
3) I am American. I was born in Minnesota, grew up poorer than almost any black person you could name, suffered from malnutrition and occasional homelessness as a child, grew up with a schizophrenic single mother who ensured that our family had almost zero support from our communities, which we normally lived in for between three to six months before moving on, never to see anyone we knew again (I've lived at 57 separate addresses, not counting when we lived in our car). The police came to our house/apartment more than once, even arrested my sibling, a Caucasian minor female child. Child Protective Services more than once tried to get my sister and I away from our mother but she always moved before they had a chance. I almost escaped once when I was fourteen, by calling the police to have them pick me up, but my mom arrived first and whisked me away. If my background shows even a hint of the "white privilege" I supposedly experienced, I'd love to know where, because I can't see it. I have never met one person of any race who has personally experienced the terrors I lived through as a kid. When I read memoirs written by abused children, I often find myself mentally competing with them, thinking, "Ha! That wasn't so bad, I've experienced worse." Moreover, it doesn't bother me now. Even as a child, I didn't notice so much because to me, my life was normal because it was the only frame of reference I had. This, I hasten to add, does not mean I haven't read of examples that are worse, I have, it's just that it takes some looking to find them. More importantly, we make of our lives what they become. The end isn't determined by the beginning. To dwell on the past is to destroy one's future. It is for this reason I feel that, even if all the claims of racism were true, and I don't believe they are, it would be better to look forward by constructively working on solutions.
A last note on this, how is it that a protest over the death of one man who dies in police custody can result in the deaths of nine innocent bystanders or police and the crowd's only get bigger, louder, and angrier. Surely by now they would realize that the only appropriate reaction would be to bow their heads in shame, apologize, and meekly volunteer to rebuild their communities and repatriate all the stolen goods looted during this unpleasantness.