1. About the Tactics card "Ambush":
1.1) May I use it when my hero moves into an area containing another friendly hero and an enemy hero?(the area contain one of my heroes and a hero(my hero) moves into the area)
Ans: You can only use this card when an ENEMY hero moves into your hero's area.
1.2) If I use this card in a Quest Phase and the enemy hero survive, can he then move to other areas, attempt a Quest, or start another duel?
Ans: No. A hero can only duel OR attempt a quest once during the Quest Phase.
This card in essence lets you stop an enemy hero from doing anything else this phase.
1.3) If the hero, Sir Valadir uses his special ability(train and then move 1 area) and moves into an area containing my hero, may I use this card to force him to duel?
Ans: Yes you may do this (assuming that Sir Valadir is an enemy hero).
2. In "Duel" Quests, if both the neutral unit and my hero are defeated in the duel, do I complete the quest?(may I receive reward?)
Ans: You would receive the reward, and then the hero would be defeated.