i believe Jaime would fight, but not for Tyrion, Cersei would do anything to kill Tyrion and probably use a humungus knight or something like that, and Jaime can bearly fight Bronn, it would take him years to learn, Tyrion has like a month tops (besides in the trailer of the season there's a fight between the prince Oberyn and some enourmous guy, my guess is the mountain, maybe that's Tyrion's trial)
The training of Jaime is all about he's ashamed he can't do the only thing he was good at, fighting.
I don't believe there's any redemption from Locke, it's quite clear that guy is some manipulative sadistic asshole, he would do anything to bring the Stark boys to the Bolton's keep.