Are there any calculations involved for designing pulse jets? Are there any requirements for calculations to determine things like exhaust length, combustion chamber size, etc? Also, does the end of the combustion chamber need to be a semi-sphere, or can it be flat?
YES

There are calculations involved in the design of a pulse jet. (title question)

YES

There are requirements for calculations... (first body question)

NO  

The end of the combustion chamber does not need to be a hemi-sphere. (second body question)