Those are good questions and I'm not an expert. I was a part of a discussion once where someone mentioned that faraday cages mostly work for signals entering.

However:

1a) You don't know (because your phone can pretend to be off). You need to remove the battery (and also remove hidden batteries)

1b) some phones support NFC, which can theoretically be used when the phone is off.

2) I suggest being familiar with: https://en.wikipedia.org/wiki/Faraday_cage and your cellphone before making a decision

3) I don't know, but this would help with #2