It doesn't matter where you are transferring from that will really impact your application. What will matter is the major you choose, the quality of your application (GPA, etc) and whether you meet the requirements for admission to both the university and your planned major.
As a lower division transfer (under 60 credit hours, per FSU's discretion), you would have to meet both the transfer requirements- a 3.0 GPA on all college coursework and a 3.0 on all coursework attempted at your last college (FSU Admissions | Transfer | Admissions | Transfer Requirements
). Since you say you'll have 3 Bs and a C, that's below a 3.0 GPA, so you would most likely not be accepted.
1) You apply as a transfer student. FSU Admissions | Transfer
2) You could apply for as early as Summer 2013, however if you slacked in high school, as you claim, and
you don't have a college GPA of 3.0, you're not going to be accepted without your AA. If I were you, I'd get your AA and then transfer. It just makes things so much easier, especially
given what you've said here. From your plan though, it looks like you'd be aiming to transfer for Fall 2013, although that seems a bit unlikely, honestly.
3) It really doesn't matter where you transfer from. While TCC would probably be slightly easier, as that's considered FSU's "feeder" school, it ultimately depends on the quality of your application. It's not like your admissions officer is going to look at your application and go "oh, this is from FGCU, they're not getting in before this person from TCC."
4) I don't know. I will defer answering that to someone that knows about that subject.