No, absolutely not. They detect them most often times even before they can be felt. Mammograms are the safest way we currently have to detect breast cancer and catch it early when the chances of cure and survival are the best. Mammograms are recommended annually for women over 40 or sooner if there is a family history.
No, mammograms can detect breast cancer, but they don't cause them. Family history, being overweight, smoking, not exercising, etc., are all different types of things that do though cause breast cancer.
Mammograms can actually increase the risk of breast cancer! A woman should get them when a lump, or abnormal leakage is found. Annual breast exams are recommended for women who are at risk or for the ones who are middle aged and older. Mammograms outside of this are the risk.
Mammograms are a way of catching cancer actually. Much like x-rays, they are a source of radiation and in the case of having a mammogram daily for years, the radiation might cause cancer. Otherwise it's fine and there's nothing to worry about.