1. When characters proceed to encounter of an adventure, do they completely reset as far as health and fatigue or just get their feats back?
All is explained p. 18 :
When players transition from one encounter of a quest to another, they perform the following steps:
• Heroes keep all damage suffered during Encounter 1.
• Heroes recover all fatigue suffered during Encounter 1.
• Heroes keep all conditions they had at the end of Encounter 1.
• Each hero player flips his Hero sheet faceup.
• Heroes keep all search cards; any flipped cards remain flipped.
• Any knocked out heroes may perform a stand up action for free.
• The overlord player keeps his current hand of Overlord cards.
• Players disassemble the map for Encounter 1 and refer to the Quest
Guide in order to set up the map for Encounter 2.
2. Getting stunned, does that eat your ENTIRE turn to get rid of or just one of your actions? If it does eat your turn, can the overlord play cards still to continue his turn? Example, monster drops stun and then plays dash to get a move action, yay or nay?
Stun only "eats" your first action to get rid of the condition. Once you don't have the card/token anymore, you still have an action available.
In your example, the stunned monster spends one action to get rid of his "stun" condition, then can make his second action (move, attack).
The answer is in the FAQ (link here) :
Q: Does the Stunned condition take away a figure’s entire turn?
A: No, the Stunned condition causes a figure to use its first action to
discard the Condition card. After a Stunned card or token is discarded,
the figure is free to perform a second action. If a figure becomes Stunned
during its turn after performing its first action, its second action must be
used to discard the Stunned card or token.