If I buy a cell phone in Europe, will it work in the US?

Technically, yes. TMoblile uses the GSM standard, which is what Europe uses. The difficulty will be that many cell operators lock their cell phones to their service. You have to have them unlocked, which voids the warranty, or check w/ TMobile and get their recommendation. BTW, American cellphone companies subsidize the costs of buying cellphones to make them affordable. They make up the difference w/ the mandatory 2 year service plan. That is why they are locked.