Okay. 2 problems here.
First some history on the bike. The 02 is the first year of the bike. Great bike, but they did have airbox sealing issues that cause motor problems. make sure the airbox intake has been resealed, had the honda update or aftermarket product to cure that problem.
It would not hurt to check the valve clearances, but most likely not your problem.
Popping on decel can be 2 things. First check for exhaust leaks from the head to the tip of the muffler. Second, the hotstart can be stuck open or have the cable holding it open. You need slack in the hotstart cable. when open, it causes a lean condition in the carb. If both those items are good, then adjust the fuel screw and if that does not help, up the pilot 1 size then adjust the fuel screw again.
For the throttle sticking, check your cable routing. Once verified, split the cable housing on the bars there. There is a plastic divider between them. Most likely the cable is not in the groove on one side of this divider causing the problem. After it is solved, then adjust the slack in the cables.