Should I pay Stage's fee for tickets that cost 0 after coupons?
Yes. Stage's fee applies to every ticket type whose price is greater than zero before applying any discount or coupon.
The reason for that is that those are tickets that cost money, just you, as event organizer, has decided to make a discount. They are not really free tickets.
But we agree that there are many situation in which you need to give some tickets for free to press, friends or sponsors, so we will implement some kind of Invitations in a near future (sorry, no ETA right now).