Can American League teams pinch-hit for the designated hitter?

Of course, but they would remain in the position of DH throughout the game. If they send their designated hitter into the field, however, then they would lose the DH and the pitcher would have to bat.

Yes they can, and some times do depending on the situation. The coach can even have the pinch hitter take the field but then he'd lose the "designated hitter" spot and the pitcher would hae to bat.

Yes, but the original DH will not be able to play the rest of the game, just the same as any other player who is pinch-hit for.

Yes

Yes. The only limitation on the DH is that if the player who starts as DH is moved to the field, the team forfeits the DH, and must have the pitcher bat.

Yes, except the designated hitter has to make at least one plate appearance unless the starting pitcher is changed before the designated hitter comes to the plate.

Yes, you can pinch- hit for anybody

Yes.

But if the D.H. has to come in to play in the field, the team loses the D.H. and the pitcher has to bat.

yes, so can national league teams when they have one in interleague or the world series

yes