FFVI Worlds Collide

Phunbaba: Gogo/Terra/Celes faced him in Kefka's Tower.  He blew away Gogo and Terra, removing them from the party after the fight.  This seems like a bug.  (Gogo and Terra weren't available during the final fight, but warping out of Kefka's Tower made them available again.

That is not a bug. Bababreath removes party members. You can either try to continue on or go back and reform your party. I will probably add an option to not shuffle/randomize phunbaba3 though because it seems controversial.

Airship: Holding the 'move forward' button (A) doesn't move the ship forward, but 'sidesteps' or strafes.  This felt jarring compared to normal FFVI.

I have not heard of this happening before. Are you sure you were holding A and not Y?

Dragons: Should they be randomized as enemies?

Do you mean in normal random encounters? They are shuffled/randomized amongst themselves based on the boss battles option chosen.

Burning House Bombs: Should they also be randomized as enemies?

Yes. I am working on an option to randomize (nearly) all fixed encounters that cannot be avoided with moogle charm.

Kefka: Should Kefka (Narshe) be fightable in Kefka's Tower?  This is some combination of awkward and LOL!

Why not? All bosses except the final battles are shuffled/randomized.