1. I'm not exactly sure, so I will let someone more experience answer.
2. Yes they can, however you have to be immediately present when they are doing so. And always have your suppressor paperwork when you take the suppressor out. Make several copies and keep one with the suppressor at all times, leave the original in a safety deposit box.
3. If it is not a trust with other people named as trustees, it can not be handed down. If you want to hand it down to children or give it to someone else, you should go the trust route and name them as trustees as well (meaning they legally own the suppressor as well). If you don't go that route, I am not exactly sure. I could take a guess at what I am 95% sure is correct, but I will hold off and let someone else get it 100% correct.