Its pretty easy to compare this character to someone with a lot for rage, she lost her father to a psycho who also ruined her face forever and she hates Damian Wayne. I could easily see this girl as a red lantern and also the fact her name scarlet kinda supports it :P

Yea, it could work.

Meh, I would prefer that the Bat-Family fix her face, & she & Jason continue to be a team. Maybe even have them get together.

Both her & Jason should continue to be more brutal in their methods, so that maybe both the red & yellow rings pursue them.