1.Where are enemy leaders placed after they are eliminated?
Back in the box.
I'm not sure that they do go straight back into the box.
On page 9/10 the rules say "If all the non-Leader enemy forces are destroyed the enemy immediately leaves the Battlefield. Do not treat the leaving enemy Leader as destroyed for purposes of gaining Glory but you do gain Gold for the Leader"
In order to gain Gold you need to move counters (in this case the Leader counter) to the Resupply section of the map so that you get the gold in the Resupply phase.
I would suggest the same applies when a Leader is "eliminated".