an unlocked phone is a phone that can be used for any carrier. they are sold by a number of websites online. now this is the things they DON'T tell you about an unlocked phone.
1. if you buy an unlocked phone, some of the features of the carrier may not work (things like mobile to mobile, or * features, or the 3 digit number to call the carrier.

2. if the phone uses a sim card, the carrier will not be able to identify it by the IMEI number, so you account will not list your specific phone (sim card phones are identified by the IMEI number by the carrier.

So cheaper is not always better

yes, an unlocked phone will accept a sim card from any service provider in the us and some in europe.

the term unlocked means that the phone will work with any carrier that supports it, so if t-moble uses this phone ur card should work