Inheritance/Tokens: The card Estates are copying has been set aside, and Estates are looking at it, not the pile it came from, so no token abilities.
BoM/Tokens: You first play BoM, getting its token stuff, then play at as something else from the Supply (so you can't play a card from an empty pile, and you only get the currently exposed card from a split pile), and since you're looking at a pile, you get token stuff.
BoM/Conspirator: You first play BoM, which counts as playing an Action, then you play it *as* Conspirator, which is your second Action played.
BoM/Procession: You play BoM as some card from the Supply twice (same card both times). Procession takes a quick coffee break, smokes a cigarette, and when it comes back, the card it played has been trashed. Wait, what was it again? Procession checks in the trash, and behold, it's a Band of Misfits. Gain a
Action.
BoM/Disciple: You play BoM as some card from the Supply twice (same card both times). Disciple takes a quick coffee break, smokes a cigarette, and when it comes back, the card it played... is still there. Gain a copy of whatever BoM copied.