It may be fruitful to assume a distribution and then see how it can be determined.
Spoiler for first question
See the part in red. My calculations show that the players would definitely end the game during that phase for the starting case of all RB stamps.
I'm confused, as often. I thought we were facing one particular run of this game, and we are seeking the one case and reveal for which A does NOT announce his stamps at step 6. The phrase "starting case of all RB stamps" makes me think we have to make a general solution for all runs of the game.
I see your point. The confusion is entirely my fault. I revised the OP to remove this confusion.