stuck throttle

You say throttle is stuck, do you mean that by moving the lever at operators position it will not change speed. Or will the lever just not move.
If the lever move and will not affect speed then look for a cable clamp near the carburetor. With mower off and throttle lever in off position tighten clamp over cable. Start mower then adjust as needed.
If lever will not move at all look for kinks in cable, if any replace cable. If none, disconnect from carb, lube cable with spray lube then work it back and forth until moving freely and reconnect.

Also
That pulsing sounds like a governor problem. If you have the Briggs engine the governor sits at the front end where it can get debris in it or bent out of adjustment when mowing under shrubs etc. Check for debris in the carb area and put a tach on it to check your RPMs.

I run all Toros. When an engine begins to "hunt" for the top end rpm it is usually a symptom of a worn throttle shaft. The throttle shaft has enough play in the carb that it starts bouncing around changing the fuel air mixture and the governor then kicks in to compensate for a "false load" Just another thing to check on your engine when you look for the problem.