На оба вопроса ответ да, можете.

Выдержка из последнего FAQ на bgg:

2.5.2
Q: After another player passes, can we still use his buildings?

If another player has passed, meaning they have finished the game, and they have an unblocked
Destination card in their city with the OPEN sign, you may visit it with one of your workers.

2.5.3
Q: Can I pass the Fool to my opponent if they've passed?

Yes.