1. Regan Hamleigh in the text says: anytime during the turn can convert 3 coins into 1 VP. Is it possible to do this only ONE TIME per TURN or could I use this power for more than 3 coins??? Ex. 9 coins into 3 VPs?
You have this the wrong way round. It's 1 VP to 3 gold. As often as you like.
2. "The King will not grant an audience!" : the card says that the "ongoing" privileges of advantage cards are cancelled for the NEXT round.
What is the meaning of "next round"? Is it the round just beginning, or the next one as the event card of wall collapsing?
The current round is nearly over. Workers and master builders are already placed.
Next round is next round.