If you don't mind the noise then you don't have to put the muffler back on, but your neighbours might feel differently.
I also doubt that much/if any damage was done to the valves after running it for such a short time. You will need to ask someone else about carb problems for this engine, my experience is limited to a handful of side valve Briggs engines, with pulsa jet carbs and a few Walbro and Zama barrel carbs. Carb issues (such as blocked passages from dirt, or stiff/hard diaphragm pump), old fuel, clogged fuel filter, and dirty/rusty fuel tank or damaged gaskets can definitely cause hard starting/ rough idling. Rough idling can also be caused by an overly lean fuel mixture.
