I’ve lost my iPhone 13 promax (left in front seat of taxi) and they have turned it off so I’ve put it in lost mode.
Are you sure that the request for Lost Mode was really received by the phone? It could not have been received if the phone was turned off. If that was the case, you would see "Pending" displayed when you check using Find My.
If I buy a new iPhone in Mexico will there be anything different than buying it in the US?
If you buy the iPhone in Mexico, it will have no warranty if you take it to another country......something that might be very important to you.
My phone company is T-Mobile. Can I register it with them and keep the same number?
Possibly, but you would have to buy an "unlocked" phone in Mexico and hope that T-Mobile would be able to set it up when you got back to the U.S. To be safe, you would really need to call T-Mobile to confirm.
I doubt that you could buy a phone and have it work while you are in Mexico and then have T-Mobile set up the phone when you returned home......because the phone would probably be locked to the Mexican carrier.
Whether or not you could actually buy an "unlocked" phone in Mexico is also open to question.
Unless it is a dire emergency, I would hold off on trying to buy a new phone until I got back home.