New York, remember? The State that looks at the Second Amendment as an aspirational guideline. To be frank, I think the current problem may be a symptom of the other.
(Unarmed populace -> Corrupt cops)
Power dynamic changes a bit, taking one down a few pegs when everyone else in the room is packing iron without having to get a blessing from the Police.
Not even a bit. If the officer is never held accountable, they can threaten with their gun and the civilian who wants to pull theirs in response is just going to be legally shot by the threatening officer (and if not, found guilty of murder by a vengeful police department). This really is a problem of accountability, which guns don't bring except in a revolution.