1. after iroh failed at his seige of ba sing se ozai tried to convince his father to let him take the thrown. azulong (i think, if not ozai's father) refused to let this happen so
2. ozia did in fact kill his father. well at least we think so, never 100% confirmed but it was pretty obvious. that is why he took power instead of iroh
3. make him more mysterious? i don't know they just decided to.
4. i have no idea what you talking about. might need to be a bit more specific
5. probably just to seperate her from other firebenders, make her more unique and more of a threat
6. that is speculation. while possible that wasn't really a question and was not shown in the series so yeah...don't know what to tell you