not a teacher
1. Peter could not get it out of his head that his girlfriend has left him after so many years. (I am wondering if If I need "it" in this sentence)
2. She has put it into her head that she needs a plastic surgery.
3. His novel stands head and shoulder above others.
4. Fame went to the singer's head, and he began to abuse people.
1) More correctly "…had left him…". You need the "it".
2) More naturally "She has got it into her head…". Delete the "a", "…she needs plastic surgery."
3) The form is usually "head and shoulders". More naturally "… above the/all/many/most others."