I'm sure this has been covered, so my apologies...
Regarding Deadman.

If I successfully manage a Possession attack, and immediately release the target after the resolution of the action I assign to them...
does Deadman come back onto the board with or without tokens?
The write up on the card doesn't mention it at all, and it came up last night.

Thanks for any help,
Dan

He would have his token from the Possession as there is nothing special which would clear him differently.

He should still have a token as he preformed a non free action this turn.

How about if Deadman holds onto a fig and releases after the figure has acted a second time? Does deadman come back onto the board with the original action token?

Deadman clears when he would normally clear - at the end of a turn during which he has not taken a non-free action.
In your case, Deadman would retain the token, but would be able to clear it at the end of the turn unless he decided to take an action after releasing the Possessed figure.

Ahh thank you