Re:Q: Recruiting using cards
"Can the FP use Strategy Event cards to recruit in settlements, if the enemy controls the settlement, but doesn't have an army there? "
No, you must control the area to recruit there.
"Certain cards allow you to "burn" a dice in order to remove event cards that are in "play". For example, a "Power Too Great". When you "burn" the dice, does that count as an action, and then the turn switches over to the other player?"
Yes, it counts as an action.
Both these are in the FAQ.