I don't think Red is necessarily Liz's father. Yes, he has burn marks on his back and the obvious conclusion to draw is that he's her father. But, I don't think it's that simple. I suspect that there will be another twist.
Everyone thought that he was her father right from the beginning. So, I don't think they would give that easy an answer.
I find it intriguing about Berlin, and what Red has to do with that. How is he connected to what happened to Berlin and Berlin's daughter?
Who is Berlin's daughter?
So many great questions to answer for next season!
And, btw- isn't the actor who plays Berlin one of the bad guys from the movie Fargo?
As far as Tom's death - it just seemed like there was a struggle for the gun and it went off during the struggle. So, in that sense, Liz did kill Tom. She didn't have to "finish him off" because he seemed to die from the bullet that went off during the struggle. I'd have to watch it again though.