I'm facing Vergere who is behind to a Kel Dor Bounty Hunter. (Both are next to a pit), I levitate Anakin who runs up to force push the kel dor into the pit. He fails the save and is defeated.
Does Vergere take the Self Destruct damage from an adjacent bomb that goes into a pit?

Well, yeah. It is an adjacent square after all. You kind of over thought this one.

Agreed. I did over think it. Once again at fault for putting real world logic in a game.

When you fail a pit save, are you defeated in the square you start in or defeated in the pit square? (Irrelevant in the given example since presumably they're both adjacent to the pit.)

In the pit.

Self destruct doesn't activate until after you have moved some one with force push right?

Damage resolves first.

Damage resolves first, but if death comes from moving into the pit instead of the damage, self-destruct happens in the pit.