If I Buy A Factory Unlocked/GSM Unlocked Iphone 5, Can I Use It With T-mobile?

I'm not exactly sure what factory unlocked or GSM unlocked mean, but I just want to know If I can use the phone with T-mobile or if I'd have to switch carriers.

Yes, you just install a T-Mobile SIM
but be warned, you will be limited to Edge (2G) data speed

Yes you cand if the phone is unlocked.

Yes you just need the SIM for that carrier and you can use it in a factory unlocked iPhone. Factory unlocked refers to the fact that you can use any GSM carrier SIM in your iPhone worldwide (as opposed to locked which means only 1 carrier SIM )