My interpretation of question 1 above, is that moving the fairy is a MTW action, and therefore cannot be done in combination with any other MTW action (such as placing the barn).
Agreed. However, I would also say that moving the Dragon is a MTW action and therefore cannot be done in combination with any other MTW action (such as placing the Builder, the Pig, and also the Barn.) Unfortunately, you can now move the Dragon and then deploy either the Builder or Pig (and the question about the Barn is pending.) Additionally, you are also able to play a Tower piece following placement of a Volcano tile.