In terms of your first point, Jaime killing the Mad King served his conscience and his dad and there's a conflict for his character because his dad's interests did not serve his conscience in this instance.

jaime is obsessive about Cersei, but not as much possessive...not nearly as possessive as she is of him. And here's an aside, Jaime didn't rape Cersei in the Sept next to Joffrey's dead body in the book. That was a highly controversial embellishment of the series. But what you do have in the book that you don't get in the series, is Jaime musing at joffrey's death that he felt nothing for Joffrey as he was dying. Joffrey was only something that dropped out of Cersei's c**t to him. Yeah, that was pretty much the writing on the part. Cersei was screaming but to him Joffrey wasn't his son, he was only something that dropped out of Cersei's c**t.

The part where Brienne and jaime hook up in the series was also controversial. There's was nothing in the book to tell anyone what to think about that because the plot had gone well past where the books left off... but the generally consensus is the show disgraced Brienne by having Jaime giving her a pity fuck and then leaving her for Cersei and then showing Brienne weeping for him. People seemed outraged that BandB had turned Brienne into a pathetic character.