I'm an immigrant, I didn't pay the bill from T-Mobile. Does it affect my Naturalization Test?

It might... something like that will go on your credit history, and they will check things like that. Is it enough to cause problems? I don't know... but if they have anything else that is negative then its more likely. Being late on a payment if far different than having one you refused to pay that went into collection. Refusing to pay it is far more serious. I would recommend paying that bill... as soon as possible.