I just have a couple of quick questions for you. I would like to know if it is common to break the cylinder head where the exhaust screws in. This has happened to me on two different engines. Is there an easy fix? If not, is it ok to run the engine with no exhaust? If it is ok, would I have to make any adjustments to compensate? Thanks in advance.

It is common to break the head when you hit the ground with the muffler, sorry we can't make them strong enough to survive the hit.
You can run without a muffler but expect problems with the idle. Better to put a fitting into the hole and use some high temp silicone tubing for an exhaust.