Can the Powder Tower be used while its owner is bewitched?
No one can use the Powder Tower this turn.

The Thief can't use the Powder Tower, because he's bewitched he loses his turn after taking his action (choose 2 gold or 1 card).

As the Witch, when you bewitch another character you still play with your own city. Since the Powder Tower is not in your city, you can't use it.

A quote from the rules that best describes this:


  When the bewitched character is called upon, its player must show his character card, take an action, and then immediately end his turn. [...] You now resume this player’s turn as if you were playing the bewitched character,
  using all the character’s powers in your city. You still build districts from your hand of cards and pay with your gold (including taxes).