1) If you have a warranty, try and go to the store you bought it from. They might replace the battery depending if the warranty has expired or not. If not, you might have to pay a bit to replace the battery.
2) My friends have a Dell DJ and like it. I know it's cheaper than a full iPod but I don't know how much. There are others but I'm not sure of them.
3) You can try but it's usually really hard. iTunes has its own code that many other mp3 players may not like. I know a few people complaining about it because they can't figure out how to burn TV shows/movies onto a DVD. Then again, I could be wrong about the first. I don't use many mp3 players often.
Hope that helps!