Can an ovarian cyst rupture? what are the signs and symptoms of having an ovarian cyst and what are the dangers ?

Yes: Every month when a woman ovulates there will be a cyst on one of her ovaries at least 2 centimeters in diameter. That cyst will rupture to release the egg. Most women do not know this has happened, but some women will have cramps or pain around the time of ovulation. Sometimes the cyst will fill with blood and be very painfull, usually it resolves on its own - but some will require surgery.

Yes, with pain.: An ovarian cyst can rupture and this can cause pain which may be significant. Another complication (much rarer) is ovarian torsion where the ovary twists on itself, causing lack of blood supply to the ovary. This, too, can cause significant pain.