The first thing I see is that this might be a short barreled rifle with this configuration instead of an AR pistol. You might need a pistol buffer tube with a pistol brace on it. Otherwise, it may be an NFA firearm that requires registration and a tax stamp. I am not a lawyer or an NFA guru, but it sounds like it could be trouble in it's current state. I hope I am wrong.
I know that doesn't answer your questions that you came with, but others may be able to look at you pictures and tell you what you need.
Edit:. NFA = National Firearms Act https://www.atf.gov/firearms/firearms-guide-identification-firearms-section-5