When babies hit their heads with their fists, does it mean their annoyed or frustrated? Is it normal?

Hi Stan, then I think it could just be a phase she is going through (sounds cute actually!). I would suggest monitoring her for a while. I only read that hitting sides of head (above the ear) could be a sign for ear infection. Otherwise, most babies would grow out of such behaviour. If you are worried, call your doctor for his/her advice. :)