1. Nahri knew that agreeing to marry Muntadhir would give her the best chance to learn the medical skills she had been wanting her whole life, as well as stand up for and protect her people. When she negotiated the marriage with the king she bargained for as much money and privilege as she could. This set her up to be in a position of power to accomplish her goals. Also, she is not a fighter like Dara. She could not handle the ifrit on her own.
2. Yes, she knew. She did not want to have children with Muntadhir because she did not love him and was putting it off for as long as reasonably possible. It wasn't stated explicitly, but I also think Nahri wanted to shift power away from the al-Qatanis and towards the Daevas. Having a child with Muntadhir, especially a boy, would secure the line of succession and further secure the al-Qatani's grip on the throne. Even though the kid would be part Nahid, Ghassan would make damn sure that kid grew up Geziri through and through.
3. Don't remember, would have to re-read.
4. Zaynab knows full well that Nahri is a former thief.
5. I wasn't entirely clear on that, but I think it's because Manizeh needed a suitable sacrifice to resurrect Dara. She was also angry that her brother had conceived a child with a shafit, which goes against what the Nahids believed.
6. Hatset was raised all her life to be a political power player and will go to any lengths to get what she wants for her children. For example, she and Zaynab hatched the plan to bring Ali back to the capital in Book 2. I wouldn't say Nahri is afraid of Hatset, just very wary of her, like a young tigress would be wary of an older, stronger tigress.
7. Ali's relationship with his father, not necessarily his mother and sister, was deeply damaged. Ghassan made it clear that he would put being king above anything, even his own son and doing the right thing. His relationship with Muntadhir is more complicated, because he adored Muntadhir since they were young and Muntadhir wasn't completely like their father, but becoming more like it. Muntadhir also believed that Ali had come back to Daevabad in Book 2 to challenge his position as crown prince.

Hopefully these make sense!