Am I a man or am I a muppet? If I'm a muppet then I'm a very manly muppet!
1. During the final turn of the game, a player fills the last seat on the board without creating a "single nation" table. Does this player still have to draw a replacement tile which will count against her in the final scoring?
Yes. They play, draw & take the -5 (or -10 if the tile is wild).
2. When jokers are played in such a way that they score at two tables, they are not allowed to change nationalities. When such a joker is later replaced, can it be replaced by an appropriately-gendered tile of either nationality? Or do you have to match the nationality which was selected for it by the original player?
Jokers can be replaced by either nationality.