1> If conditions are ideal, could be several hundred feet.
2> Yes, a neighbor can definitely use your wireless connection if it isn't configured correctly.
3> To prevent this from happening, you need to disable broadcasting of your SSID (Network name basically) and also enable encryption. This way they won't SEE your network, and if they were to discover it, they still couldn't connect because they won't know the password. This should all be explained in your router's manual. If you don't have one, go online and download one.
Keep in mind, if a serious hacker wanted to target you personally, they'll still find a way in.. but a neighbor wanting to piggyback on your internet won't be able to anymore.