Are breast cysts dangerous?

Not at all. Breast cysts develop when a milk duct gets obstructed & accumulate fluid, forming a "water-balloon" in the breast. As many as 1/3 of women between 35-50 will have cysts. The main problem with cysts is that it is impossible to know if a new lump in the breast is a cyst or a tumor w/o an ultrasound or a needle aspiration. Therefore, never assume a new lump is a cyst until proven otherwise.
No. If it is really a breast cyst, these are not cancerous and generally do not cause problems. A true cyst, by definition, has a negligible chance of developing into cancer.