During Mystery phase when minions move or are placed at same spot as Heroes must they fight during the Mystery phase?
Yes -- Heroes always fight immediately whenever a minion appears in their space. The rule is on page 17, right-hand side. The only exceptions are:
-- No fight if the hero is already knocked out (but you do fight immediately when you "wake up" if the minion is still there),
-- If there is a hero with higher honor in the same space, then that hero fights first, and you only have to fight if the 1st guy loses or runs away.
-- Some minions (like bats) don't "fight" at all, but you still encounter them according to the above rules.