Who's your carrier? If it's not Verizon then why would it matter that you have the Verizon or T-Mobile one?
For returns I think you have 30 days for iPhones to get your money back. I assume you could return it and exchange for the different carrier version if necessary.
Probably not if you're past your your return window. You probably have to do a return and buy the model you want. By the way Apple has reduced the return window of iPhones to 14-days in the US.