Should sharpening nicked knives with whetstones leave the nicks in the blade?
You are indeed supposed to remove so much material from the blade that the nicks disappear completely. You'll have to lose what's probably a least a milimeter of the blade's width. 

For that, the 1000er grit is indeed too fine. Go for something much coarser, and use finer grits for finishing. With the stone you're using, you'll have to spend days to get so much steel ground away. Something in the 150-300 range will do nicely for the task you have.