1) Fortune and Reputation are not listed on p. 21 under "Game Carryover", so no, you do not keep the remaining tokens.
2) Correct as far as I can see in the rulebook.
This is correct. Nothing you possess carries over except those things explicitly stated in the rulebook.
You only take rep/fortune from supply at the start of the game, or when instructed to by an effect or the captain's booke.