Why don't you lift the rear wheel and peddle by hand until you see why it does not run properly on the sprocket. You should see the chain bind or a part of the chain that seems to not follow it's path.
As for throttle, I always run grease and oil along the inside cable after removing it from the housing. There is no reason for a stiff cable unless it's bent or kinked from how you ran it. I also grease the inside of the throttle housing. I think all, if not most of the sellers will sell you a new one for a few bucks.