Not likely. You have millions of unfertilized eggs in each of your ovaries, the size of the cyst varies greatly, and size of the cyst will determine the degree of pain and disruption of other bodily functions. The rupture of a large cyst can cause several short term problems but should not affect fertility unless excessively large. Please discuss this with your personal OB.
Shouldn't. Every month when you ovulate that's actually an egg cyst rupturing and releasing the egg. You probably had a larger cyst that ruptured causing more than usual pain. Every month you will produce 3-5 egg cysts (AKA follicles) and usually one ruptures. You couldn't get pregnant without this process.
No. quite common and no lasting effect.