Interesting questions. It prompted me to revisit some of the actual rules. The one caveat though is that all I have are English translation rules from RGG. They may or may not be universal. I know what you're thinking - "lot of help that is". Anyway, here is what I found. I guess it matters what side of the pond you're on...or if you plan to play international tournaments

3. The Princess and the Dragon: Suppose that there are two followers on a tile (due to a tower, or other reasons). Does the fairy protect all followers on that tile from the dragon?
The original instructions state that the player moves the fairy to any "tile" where he has a follower, and that the dragon will not visit a tile that has the fairy. Thus, all followers on this tile are protected from the dragon.
Are all the followers also eligible for the start-of-turn point bonus?
The rules also state that if a player starts his turn with a follower on the "tile" where the fairy is he scores 1 point. This indicates that the fairy is not on any particular feature. We play that the Fairy's area of affect and protection is the whole tile.
4. Bridges, Castles & Bazaars: What happens when a bazaar tile is drawn as the first tile of a builder double-turn? If an auction ensues, does the player that drew the tile proceed to draw a second one due to the builder, and then the next player lays down the tile won from the auction?
The rules for Traders & Builders regarding the Builder state that the player shall complete his turn (of playing the first tile), then draw for his second turn. Unfortunately, BC&B does not mention the Builder. It is reasonable though that the auction, and placing of the auction tiles, is the resolution of the first turn. I would think the second draw occurs after the resolution of the auction. This is the way we play it.
5. Bridges, Castles & Bazaars: Suppose that no player wants a particular tile. Who gets it? Does the first player to the left have to bid zero as the first bidder? What happens then if all the others pass? Is the first player stuck with the tile?
The rules for BC&B state that the auctioneer "starts the auction by saying how many points he will bid for the tile (he can bid 0 points)." I believe the intent is that he must bid at least zero points, as opposed to "pass". Note that a player may also go "negative" to buy a tile.
6. The Tower: Suppose that you have less than three points on the scoreboard. Are you still allowed to pay the ransom and get back a prisoner captured by a tower? i.e. Can you temporarily have negative points as a result?
The rules for the Tower state that if a player does not have 3 points to give, he may not ransom back a prisoner.
7. Bridges, Castles & Bazaars: Can a mayor be placed on a castle, or does it have to be a regular or large follower, in order to obtain points for the surrounding feature that is scored next?
We play that technically a Mayor may be placed on a Caslte but would score no points as he has no scoring power unless he is in a city with a pennant. He does represent a presence and ownership however, although I don't know what value that would have in a Castle. We play that he could be used to cap a Tower, for example, or claim a feature so no opponent may enter it directly.