I have a ganglion cyst. If it burst would it cause sharp pain?

Doubtful. In the old days, it was called the "bible" treatment to rupture a ganglion cyst on a person's wrist. As the bible was usually the biggest book in people's houses, it was told to people to swing it hard against the wrist to rupture the cyst. The blow I'm sure hurt more than the cyst rupturing.
First the relief. Typically it would hurt at first but then you might experience some short term relief.
It can. I have had patients complain of pain for a couple of days after a spotaneous rupture of a ganglion. If it persists I would have your doc evaluate.