IF the projects aims to raise much then they have to spend some right? So yes they are going to pay the transaction fee which may cost few hundred or thousand bucks but they will get in few hundred or million bucks so totally they are going to be in profits. 
I would agree and considering how much they got in ico, it's just peanuts to them. While the fact remains that's the least thing they can do, I mean for sure participants can't sell their token in decent value.Anyway, I'm sure they're using mass sending software, don't know what specifically but they'll definitely don't want to over spend for just a transaction fee.
Gas fee can be $0.20 so how expensive will an airdrop be?
Guess that's too much, typically it cost them roughly $0.03.