Believe it or not, squids expel both :) They have a little siphon near/under the "cap" that they use to expel water for locomotion (as seen in the primary mechanic of this game). I believe the ink comes out the same siphon when the squid wishes to expel it.
I agree with you and the other commenters that mentioned how hard it is to put out the flames. I think the biggest issue is there's very little feedback other than the black smoke that the fire is taking "damage". Hopefully once judging is over I can get back in and fix some of the more frustrating bugs and clean up the sound/add music.
I really appreciate you taking the time to play and comment!