I don't think anyone should be "documented" in the governmental sense, but I do value identity and reputation and the open roles they play in a free society.
As for someone purchasing a device directly designed to kill and excellent at offensive force (i.e. violating the NAP), I think we should at least care about some things such as their mental state, their training level operating it, their stated intentions on how they plan to use it, etc. I'm not talking about a top-down, authoritarian 1984 style overwatch or something, but just common sense because we don't want innocent people to get shot up.
I wouldn't let me 4 year old drive a car. I also wouldn't sell a community member a gun if their intention was to go violate the NAP and shoot someone.
When it comes to "gun control" and "gun regulation" I'd hope the voluntaryist community would be huge supporters but in a completely different way than what is represented by the media. I'd like to see communities training each other how to obtain and use firearms for personal defense while holding each other accountable for safety and security. As most serious gun owners will tell you, many who own guns now (especially if they have kids in the house) are some of the safest and most regulated (and by that, I mean self-regulated) people around when it comes to guns. Their kids have been well trained and understand the serious dangers involved. That's what I'd like to see more of because that, to me, is rational personal responsibility which can be encouraged through healthy community.
For sure. I think the free market would take care of a lot of these issues. And by that I also mean community. Who is going to want to associate with or do business with a shady fellow who moves in next door and starts stockpiling rocket launchers while maliciously leering at everyone everyday? He'd be driven out via social pressure/ostracism/economic starvation, I'd guess, if he could even "move in" in the first place (a land seller would likely have several background checks in place).
As for regulation now, yep. Most folks I know with guns are very responsible and caring folks. I grew up with guns in the house as well, and was taugh that they could very quickly end my life and were not toys.
Property owners would ultimately have to decide the type of people they'd want to live around, and could even make rules to government what's allowed/not allowed on their jointly owned properties.