Hi just got this game. On our first run through the missus and I got in to a situation as follows. I am the ds defending, she is ls attacking. We play the edge cards then reveal, we both have played fate cards. I played heat of the battle which is initiative 6 and kills her only attacker which is jedi in hiding. She played target of opportunity which comes in after my fate card has already killed her attacker. The question is does her fate card take effect (as she no has no attackers)

Another question while I am at it is, on (her) next turn I am not defending but she wants to still play edge cards. How does that work if I am not taking part in the conflict?

The answer is yes in both scenarios. You would continue to resolve fate cards even if her sole unit is destroyed by a fate card. Your defender (s) would also still focus and resolve their combat icons or any effects they may have.

Also, an edge battle happens every battle, regardless of if there are defenders.

To clarify that second point a bit. There is always an edge battle, but if you have no defenders participating in the engagement, you cannot play cards into that edge battle, and the attacker automatically wins the edge in that case. But the attacker may still play cards into their edge stack, for example if they want to play Fate cards.