Re: Code Geass (major spoilers for Code Geass and Death Note
Kallen is a fairly well rounded character that never got the chance she should have to flourish. There is no denying that she is essentially a missed opportunity, as she was due to get a far bigger role in R2 than she did, but it was scrapped. Either way, i don't generally understand the hate she gets. Her hatred is completely understandable, and what's more if you followed the series properly, you'd realise that Her hatred for britannians is based both on a grand scale(area 11, being treated as muck under the feet of others) and family based, considering her dad is a high-ranking britannian(hence stadfield) whom she hates entirely. In her situation, considering the state of japan, it's completely understandable what drives her, what she wants most of all and the lengths she'd go to, to ensure they where met.
Let's consider your other pointers, which i feel are more directed at your distaste for lelouch rather than for kallen. Considering how much we've thrown under spoiler tags already, i'll just cover this all up with tags.
Going down the list one by one:
1. Yes, she does. But she also realised that revealing his secret would throw the Black Knights into despair. They didn't want to know who zero was either, so long as the goals where mutual, they could work together to ensure they where met.
2. She knows he's a member of the royal family, yes. But so do at least 1 or two of his classmates, as such defeating this point entirely.
3. This wasn't something she fully understood until R2 anyways. Outwith that, she'd be treated as mad for suggesting it, nearly noone knew of what a geass was.
4. She kept quiet about it, but that's because she also knew it was an accident. While lelouch is good at hiding most things, i'm pretty sure that kallen was able to pick up his true feelings about what happened.
5. Answered this already. Family ties and the suffering of a nation.
6. But this was to defend her home, to protect those dearest to her. Her reasons are entirely just in the series
7. But also caring, determined and strong willed.
8. Loves a fickle thing~
9. Quite rightly too. Suzaku was doing the exact same thing.
10. She betrays them yes, but in doing so, she tries to defend them. She regards them as important, so much so that being hated by those she wants to protect would be enough to ensure they don't come into harms way. I think that's a fairly decent trade.