Tom,
The surging sounds likes your fuel system/carb needs a cleaning. Take your aircleaner housing off all the way, with the two bolts that hold the housing on to the carb. Spray the carb down with some cleaner.
Also put some Seafoam additive in your gas tank (follow directions on can). Put all back together and run for awhile. If still surging after that you may have a leak in the gasket on the bottom of the carb.
The engine shut down could be a number of things. Since it is definitely heat-related, it could be one of the coils getting warm and failing too. That ones a little harder to diagnose.
Rattosh51
YT6800 S/N 821
St. Paul, MN