After looking closely into the order of resolution of abilities during attacks, a question about cleave came to mind. Cleave triggers after an attack resolves, but let's say an attack is interrupted by an ability like close quarters.

For example Verena is in a line with 3 storm troopers. Can Verena attack the first trooper, trigger a cleave, use close quarters/combat momentum to advance and kill the 2nd trooper, use close quarters/combat momentum again to attack the third trooper and if it doesn't die, use the cleave from the first attack since the interrupts are now done.

Similar question would occur with blast. Let's say a target next to her was killed with an attack that had blast. Would she be able to use Close quarters and/or combat momentum to move away from the targeted space to avoid blast damage?

Yes, Close Quarters triggers when the target is defeated, which is before the attack is resolved. She could move out of the Blast range using her abilities. (But note the difference in how movement points work during and outside of her activation.)

For Cleave there is a question whether "could target for an attack" would have memory or not (remembering Verena's position for the original attack), but because things do not usually have memory in this game (except the targeted space for Blast), I would be inclined to resolve Cleave from where she is when Cleave is resolved.