As far as I understand it, buying tokens on the marketplace puts those tokens into your art library, so you should be able to use them any time you could add tokens to the table:
1) If you are GMing, then you can add the tokens from your library, and assign them to your players.
2) Not currently, unless that other person promotes you to 'GM' status for that campaign, as players can not currently add tokens to the board.
3) Same answer as #2.
There has been some talk of allowing players to add their own tokens to the tabletop, but no concrete plans, as of yet.
Anyway, that's how I understand things, I'll ask the devs to weigh in if they feel the need to.