Probably not bothering a large enterprise who thinks you are cutting into their IP’s profits.

“Profits” from a game they abandoned and aren’t marketing the IP? Would be a pretty weak argument in court.

IANAL, but it’s not just that particular game, but sequels, alternatives, or the right to release a remastered version that they could claim damages on. And really they just need standing to sue to make it not worth a hobbyists time, I can’t see most of these things making it to court.

Presumably having hours when it's open to the public... but I imagine you'd need to set up a non-profit as well, in this case.

You can post "by appointment only". Hell, there are government offices that play that card.

You have to convince a human that your basement is a museum in order to make this work rather than a simple robot. A sign won't be nearly enough.

Obviously. But that doesn't help figure out where the boundary is between "collection" and "museum".

Ah, so that's what .museum domains are for.