The iPhone needs to be unlocked to use t-mobile, but it does not have to be jailbroken. Bear in mind, that the internet using an iPhone on t-mobile will only use t-mobiles Edge network, not their 3G network, so anything using the internet will be slow unless on WiFi. If you have a choice, the...
iTunes does a backup automatically, but if you are getting a new iPhone, they don't take back your old one unless you are at some 2rd party company so you will have both.
Probably because they bought them from iTunes or another place and their digital right won't allow the transfer. You can make your own for free at Ventones if you have the song on your computer