I want to be able to log into social networking sites like FB. Do I have to make a new account or will Tor protect my identity still? I think I logged into FB and realized that I might not be protected anymore. What do I do? Should I make a new identity and then a new account?
When you make a Facebook account and whenever you log on you give them your identity. That's kinda the whole point of Facebook.
The purpose of Tor is to make delivery of your internet traffic anonymous. Tor doesn't make the contents of your traffic anonymous.
If you have a shell account (meaning it uses a fake name and stats) and reveals nothing personal, then using Tor you can mask your location and trail. HOWEVER, keep in mind there are other ways that you can breach your security, even with a Tor connection.
For example, if you enable Flash, there are hidden flash embeds in the FB code designed to track stats, much like Urchin does but to a more unbelievably detailed level, such as how much time you spent on a page, what you looked at, where you clicked, what you clicked, if you scrolled all the way down or not, where you went next, where you came from, and so on and so forth. Among the data it gathers is your session id, geo tags, and so on. Because it uses Flash, it gathers it client side, which means its getting it directly from your system, this WILL expose your external IP, the real one, it will also expose whatever else you have exposed on your system that can identify you. To solve this problem, make sure you disable Flash while using Tor, ALWAYS - unless you accept the risks I have mentioned.
If you log in with your account, and have logged into that same account some other time from your regular connection - then you are not anonymous. If you have provided a email you also have logged into with your regular connection - then you are not anonymous, things like this can be traced.
However I think it's important to mention that Facebook has a .onion domain - https://facebookcorewwwi.onion/ , using that with the torbrowser will make sure facebook do not get what IP you are connecting from, since it's a hidden service. This is a legitimate service they provide. They will know it your account that's in use, but not where you connect from.
There is a post on torproject's blog with more information.