I have two questions:

1. In the Wanderlust ending scenario, when it says "When a character with a Path resolves the Treasure room, etc, he places his Path facedown." If the player for example fights the Eagle King and ties or loses the battle, is this Path technically resolved and can be placed face down? Likewise, if a character visits the Encounter with Destiny and has to fight, but ties and is transported out of the Woodlands, would that Path card go away or count?

2. With 'Place' cards drawn from the adventure pile, do all of those cards remain on that space for the rest of the game or only the ones that specifically state they do? My friends and I argued this last night on if a card is permamantly on the board.

I believe resolving the space means encountering the space (and not a character or dragon scale) regardless of the outcome, so yes you're right. I also think Place cards remain on the space until instructed otherwise...

1. Yes, it is enough to encounter and resolve those spaces; it is not required to win against the boss or to positively fulfill the Path's conditions at Meeting with Destiny.

2. Usually Places are meant to stay for the rest of the game. In the Firelands and Woodland expansions there are several Strangers and Places that don't have the sentence "will remain here for the rest of the game", but they are meant to stay. As a general rule, cards that don't have discard instructions do always stay on the board, regardless of the card type.