Is pid associated with cervical or other cancers? does pid cause cancer, or are women who already have cancer likely to develop pid?

Not really: These are not really related conditions. PID is caused by bacteria from the vagina ( or sexually transmitted bacteria) getting up the cervix into the uterus and tubes and setting up an infection. This isn't really related to cancer at all. The only exception is that very severe cancers can cause necrosis of tissue which can mimic infection in many ways.