Yes, but then she said she was getting back at Shinji for saving her from the volcano, so she probably wasn't grateful for that, since she sees being saved by someone she considers lower than her to be a sign of weakness, which she won't have.
Surely eliminating her debt to Shinji would be a matter of honour, though? If she had no honour, she would have gladly let Shinji take the defence position.
And, of course, that's simply how she justifies her sacrifice to Rei and Shinji, and we know that Asuka always puts on a show of being superior to everyone.
As for Shikinami piloting in Rei's place, I think it's just Asuka trying to hog all the glory for herself to feed her inflated ego, like she always has, and not out of obligation.
Perhaps, but before she enters 03, Asuka talks about how she's discovered that she actually appreciates being around Shinji and the others, so I would say that she does have positive feelings towards them - even if she won't admit it to herself.
Because Asuka being "kind" to others would be out of her character, as kindness is not in her dictionary.
Only if you attribute her acts of kindness to selfish motivations. And it could be argued that everyone's kindness has a basis in selfishness - they kind person wants people to like them.
As for her mental issues, is that really an excuse? Or is that just how she is?
An excuse? No. But it helps us understand her more - and, if people in-universe knew about her disorders, and helped her, perhaps her attitude would improve.
They may be living in hell because of him, but still, I find their treatment towards him to be inexcusable.
Inexcusable things are normal in hell.
Besides, Shinji seems to have no issue with their treatment of him after Kaworu tells him the truth.
And as for Misato thinking she has to kill Shinji, would she take pleasure in it? Maybe Asuka too? If that's so, then both of them are just as bad as Gendo is, if not worse.
No. Both Asuka and Misato are given the perfect opportunity and perfect justification to kill Shinji, and both of them choose to spare him - and, in Misato's case, she made all life on Earth at risk by sparing him. These aren't the actions of people who would enjoy killing him.