Facebook would still be able to provide the IP address in response to your court-order or law enforcement request.
Sure you can trace it back to the address.. You just need a judge to sign a court order or subpoena to force the Internet Service Provider that owns the IP address to turn over it's (very private) customer information - just has been posted/commented here on this page several other times.
No, unless you have a lot of money and an attorney.
Where did the nude pictures come from? Maybe next time, dont leave nude photos of yourself on Facebook?
Possible? Yes. easy or free? No.
Read through all of the other comments already posted and you will see how difficult/extremely improbable it is.
You would need a law-enforcement request or court-order to Facebook to get you the IP address.
Then, since the IP address alone is useless, you will need another court-order to the ISP that owns that IP to force them to turn over the customer information.
If the IP address is a proxy or not in the United States, then it gets complicated.
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