No

Only character actions (those that require you to claim a card in front of you) can be challenged.

Challenges

Challenges come first. Once any challenge has been resolved, then someone can propose a counter-action, which can itself be challenged.

Officially, whoever won the last game. Otherwise, you can choose any way you like.

Survive

By being the last player to have at least one face-down card (influence) in front of you when all other players have been eliminated.

Your cards

Your 'influence' is just the cards you have in front of you.

The game ends when only one player is left with a card in front of them.

No

You can't.

No

Not unless the rules specifically tell you to reveal a card.

Face-up

Keep it face up on the table in front of you. It no longer counts as your card, but this allows everyone else to see which cards have been taken out of the game.

Right up front

Announce the target when you announce the action, before any challenges or counter-actions are declared.

Challenges

A single action can be both challenged and (if the challenge fails) counter-acted. Resolve the challenge first.

No

No

No

No -- keep the coins you would have paid. (However, if the action is counter-acted, you must still pay. This only applies to Assassinate.)

Yes

Yes, using the same rules as for challenging a character action.

No

No.

No

No, any player can challenge any other player's action.

Sometimes

To counter-act the Assassin (assassination) or the Captain (stealing), you have to be the target of the action. But anyone can counter-act the Duke (foreign aid).

Yes

Yes, everyone can see how many coins you have.

Yes

Yes, you can be knocked out instantly by an Assassinate action. This can happen in two ways: (1) you try to challenge the player claiming the Assassin, and lose the challenge; (2) you claim the Contessa to counter-act the Assassinate action, then you are challenged on this and lose the challenge. In either case, you lose 1 card for the lost challenge and then the other from the Assassinate action.

Yes

Yes, you can choose which card to lose if you're targeted by a successful Assassinate or Coup action. You can even choose which card to lose if you lose a challenge -- don't reveal a card, just choose one to lose.

Who cares?

It doesn't matter. You are out of the game anyway!

Yes

Yes, you can swap 0 or more cards.

No

No. You can choose to swap 0, 1 or 2 of your cards (if you have that many), but other players shouldn't know which option you choose. The best method is to mix up all the cards in your hand and then choose which one(s) to keep. All the other players should be able to see is that you return 2 cards to the deck.