and the interactions between her and a female friend (I forget her name) show she's not over the trauma from that.
I honestly don't remember this at all. Do you mean her lesbian relationship with Taena and all that jazz?
When her and Sansa are in the Red Keep, she says she would rather be out there fighting than waiting to die -- but again, she was never allowed to learn how to fight.
This is a lot of the reason why I like Brienne so much. She's breaking all of these stereotypes that Westerosi society forces upon women and it's really cool to see her do that. Brienne and Cersei are two sides of the same coin in that regard, since both are trying to overthrow gender stereotypes. Cersei is the political side of the fight, while Brienne is the social.
Not sure if it's in the books (been a while since I read the 4th book) but in the show, her uncle refuses to be the Hand-of-the-King and tells her she is "The Queen Mother and nothing more," highlighting that an 8-year-old (he's 8 in the books I think, but maybe 12 in the show??) who would rather play with kittens and knows nothing of politics or ruling is better suited to rule than her just because he is her son and male.
To be fair, Cersei truly is the one ruling (in the books, anyway) and she will be until Tommen is 16, so that quote is kind of silly. I don't think anyone in their right mind would want a 9 year old ruling instead of a woman.
A quick google search says that Tommen is 9 when he marries Margaery in the books and is about 15 in the show.
Her strategic blunders all come from the fact that she was never taught how to rule because it was expected that her husband would be the one making all the decisions anyway.
I refuse to believe this. Sure, some of her missteps stem from her being unaware on what to do, but saying all of them are caused by that is a little much. Ruling a country is not easy work, but she has an entire council to get advice from, and yet she replaced all of them with idiots because she couldn't "trust" anyone else. She is an intelligent person and a lot of her mistakes could've been solved with common sense. Like, no Cersei, building your empire on lies and machinations is not a good idea and will end badly for you.