Did any such incident happen? What are the rules if a ball breaks during play?
Depending on your definition of "break" it has happened frequently: the ball can get out of shape, overly wet or come apart at the seams.
Law 5, part 5 covers what happens in such cases: the ball is replaced by one of similar wear and tear. The umpires will check the ball regularly to keep an idea of its condition.
It can also be damaged illegally, as described by Law 42, part 3. A different set of processes is used and there may be penalties applied.
Yes, Same as above if the ball tears out then the umpires will change the ball with the ball with the same condition. Moreover, i remember a test match of pakistan playing against west indies. The ball wear out and the umpires changed he ball in the 5 over of the match. So, Yes if ball wears out ball will be changed.