I probably won't be much help, but I will give it a whirl.
For your first question. It depends on where you bought the iPod. If you bought it from another store, i.e. WalMart, Amazon, Best Buy, etc. and you are within a year, then you should have no problem. You will just have to locate your warranty info and take the steps to get it repaired/replaced. However, if you bought it off of eBay or from somewhere else and it was used, then you may not have a warranty anymore. The iPod comes with a one year standard warranty and then you can pay to add additional years of AppleCare. If you live near an Apple store I would take it in to a a genius just to see what they say. I've read a lot of stories where people took their stuff in, even when it was a little out of warranty and apple took care of them, so you may get lucky.
As for your second question. It is my understanding that dead pixels should be something that you notice right from the beginning and will be a white pixel that you can see on dark colors (I had one on my iPod Touch last year and returned two PSPs because of the issue because they always pull my eye toward them and all 3 situations the problem was there from the beginning) What I believe you have is a stuck pixel and I don't know as much about them. As I mentioned I had a problem with my first 2 PSPs having dead pixels and after returning them the third one seems to be okay. However, I've noticed on my one game, which happens to be a baseball game there is an area in the upper right corner where there appears to be a dead pixel, but it only happens on that game. So I'm not really sure what is happening with my screen, but I didn't know if that may help you and if yours is there no matter what you are doing.
Hopefully this was some help!
