No, it's not normal. Sometimes girls get hormonal at age 12 when their periods are starting or about to, or in dealing with middle school drama. But you say your daughter is slowly getting over this so I imagine it's gone on for some time.
She has control issues, some sort of hyperactivity in that she can't stop talking, but she also has crying fits and is "down" a lot.
She's swearing and she's not listening to you? Not acceptable.
She may have any of a number of disorders including ADD, ADHD, bipolar, PDD, and she may benefit from evaluation. I'm surprised no one has talked to you about this if it goes on in school. She could also benefit from therapy, or from consistent discipline, depending on the source of the problem. She could benefit from better nutritional balance through effective supplementation and brain support to regulate any chemical imbalance. So there are a number of approaches to try, and with all of the new advances in nutritional support, there's a very simple place to start which is what I would recommend.
But putting up with a child who curses and doesn't listen is absolutely not going to work for you, and you need to act quickly because the more kids get into adolescence, the greater is their desire for independence and defiance and rebellion.
I really think you need to get on top of this immediately.