I bought an unlocked iPhone 3gs. It is version 5.0.1 (9A405). I can receive picture messages and it shows the battery percentage. I have an older version of iTunes so when I plugged in my iPhone, it said that iPhone can't be used because it needs iTunes 10.5 or later. I want to be able to import my old iPhone's phone numbers (should be saved with my iTunes) and music onto my new unlocked iPhone but I'm worried I'll get locked out and my iPhone wont' work anymore for T-mobile.

Can I update iTunes and sync my iPhone?