1) How many times per player turn can an action be used? I'm assuming once-per-turn, but I can't find a specific rule saying that.
2) If an action is prefaced by a location (Battlefield, Quest, Kingdom), does that mean that action can only be used if that card is placed in that location? Or can it only be used during that phase of the turn? Again, I'm assuming card location, but I can't find that in the rules.
1) There should be no limit to the number of actions per turn. Refer to page 10 of the rulebook:
Once both players have chosen not to take an action, play proceeds to the next phase.
This means, only once both player passes does play proceeds. Otherwise both players can lay down as many actions as they are able to without failure to abide to the game rules.
2) Your original interpretation is correct. Refer to page 16, under Zone Specific Effects. Location of card is the important thing to keep in mind here. The fact that Zones share the same name as the Phases is what may be confusing about the whole business.