If you are able to connect and play Empires & Puzzles from your device on WiFi, I would believe the issue is not with your account or the Empires & Puzzles application.
Most likely the issues you have experienced are related to your mobile data provider either blocking a port necessary to the game or limiting the mobile data.
I understand you have already contact T-Mobile, however, network issues are beyond our control.
In saying this, we are investigating this issue further to see if we can affect anything on this end.
As this is not a game side issue, it is not guaranteed that we will be able to affect anything from our end, but we will do our best and update you if we have new information.
We thank you for your patience, and in the meantime recommend playing via a wi-fi connection or another network if at all possible.
If you face any other problems, please don’t hesitate to contact us again. We are always happy to assist you. Best of luck in the battles!