A worn sprocket shouldn't cause a problem for a new chain... at least, not in that distance. (A knackered chain will wear a new sprocket quite fast though.)
As for shifting the nut, screwlock compounds often seem to get tougher with age. I've had to use far more force than I'd expected a couple of times and the "crack" when it finally lets go is quite alarming. If you've a butane torch, heating the nut quickly up to 100ÂșC should weaken the compound enough to make the job easier.