Not necessarily. A cyst can be caused by many things, such as infection, a blocked duct, or some sort of oversecretion. A biopsy would be needed to study it.
No, it is not. It could be a fibroid. A cancerous growth will be hard and unmoveable, whereas a noncancerous one will be moveable. A needle biopsy will give a definitive diagnosis.
Finding a cyst in your breast is a frightening experinece and immediate followup with a physician is the only way to tell if it is cancer or not. Don't delay!
Breast cysts are benign fluid-filled sacs, not cancer. However, a biopsy is sometimes needed to be sure that a lump that can be felt is a cyst and not cancer.