I don't think they can track you down (your physical location, phone # etc) equipped with only your ip address. You're pretty safe from that. But they may be able to track your actions on the internet. e.g. which sites you've been to etc with something called "cookies" I think.
Yeah you can only have an IP if you're _on_ a network. That is, either on the internet or the intranet. (Intranet is like a group of connected computers, like in a company etc)
Someone said something about ISP. Ok. ISP stands for internet service provider. You basically have to go through the ISP to access the internet. That's why you pay them money every month for the internet access. When you're on the internet, the ISP assigns you an identity, that's your IP. But lots of ISPs make your IP random every time you log on to the internet. So usually if you want to change your IP 'cause someone's tracking it just restart your computer.
I admit I'm not expert on this stuff. But 90% of what I said is probably right.