During Sauron's turn on the plot phase:
1. When a plot card is played, is the affected token advanced upon card play or upon the next turn?
2. When 3 plots are in play and you wish to discard a current plot to play a new one, is the new plot played the same time as discarding the old or must Sauron wait a turn to play the new plot?
#1: Like in Arkham Horror, MEQ is a game where "follow the phases/steps" rule of thumb works well. Advancing tokens comes first (Story Step), then the playing of a new Plot, so it will only move the token for that Plot next turn, assuming the heroes haven't removed from play before that.
#2: "During this step, Sauron may perform one of the following
activities." (p. 13)
Options being 1) Play a Plot, 2) Discard a Plot, 3) Do Nothing. In order to play a Plot you need an empty slot, so you can't discard and play a new Plot in one turn. However, there is an option with a Shadow card, Ithil-Stone. You have 3 Plots in play, use your Plot Step to discard one, then in your Action Step (when Ithil-Stone is used), you can fish out either Denethor or Saruman Plot card and put it into play.
My other question is based upon a quest. Eometh's Advanced quest has him exploring Dol Guldur. The Mouth of Sauron was waiting there and combat ensued. Both became exhausted and combat ended as did Eometh's turn. This end of combat and turn did not allow Eometh to explore Dol Guldur as his Quest requires. Here are the issues:
A. On Sauron's turn is combat required if the Mouth of Sauron does not move?
B. On Eometh's next turn if the Mouth of Sauron did not move, the Ambush step (I assume) becomes required?
C. Since Dol Guldur is perilous can Sauron choose a Peril card instead of combat with the Mouth of Sauron?
D. Even tho Eometh did not technically "explore" Dol Guldur, since he stepped within the space, does that count as exploring?
E. Should a second combat end in another stalemate, is there a way for Eometh to declare himself defeated so that he can be sent to a Haven and rest?
A: There is no combat on Sauron's turn, ever I think.
C: Only on the turn Eometh moves into DG, on the second turn (in your example), can't choose Peril or Ambush, it's Ambush.
D: No, you have to do the Explore action during the hero turn, which requires him to defeat the monster/minion in the space, otherwise his turn ends (unless you're Thalin).
E: Note that if the Ambush ends in stalemate and Eometh isn't defeated, his turn doesn't end (turn only ends if he is defeated or if he fails to defeat the monster/minion during his TRAVEL Step), he can take the rest of his turn normally. This means he can not only Explore Dol Guldur to complete his Advanced Quest (since he is already there, why not?) and continue moving, probably to Lothlorien.
Voluntary defeat requires bit more specific circumstances:
"Q: What happens if a hero has 0 cards in his deck and not enough cards in
his hand to move to an adjacent location?
A: The hero will need to rest on his next turn in order to
get more cards in his life pool. If the hero is on a Shadow
Stronghold, within 1 space of the Witch King, or does not have
cards in his rest pool, he may voluntarily be defeated at any point
during his turn (since he cannot rest)." (FAQ)