It depends on the phone and what you need it to do. First you have to unlock the phone or it won't work at all on TMob. I tried to use an unlocked AT&T 9810 on their network and it does not have the 4G radio, though it did work on EDGE. Some AT&T phones have all the Tmobile radios (I think the 9900 does), some apparently do not.
With EDGE yes. T-Mo is in the process of refarming their spectrum that will allow AT&T HSPA+ phones work on T-Mo, as well as get the network ready for LTE. I think some markets are already done, but I'm not sure if they list which ones are done anywhere.
Try popping your Sim card in and see if you can make calls and use data etc. I'm not well versed in windows phone so I do not know how to unlock or check if a lumia is already unlocked. Checkout cellphoneforums.net they have a lot of useful info on there.
Yes.
A Blackberry mobile device can be unlocked and by unlocking your Blackberry you will be able to use it with sim cards from other carriers..
But when it comes to AT&T and T-mobile.. the best thing is to use a device from a carrier that uses the same device (with the same frequency bands / radio hardware).
The things is that if you will use unlocked Blackberry from AT&T with T-mobile sim card you will have the calls / SMS but you will only get EDGE connection for data.
If you want to take a Blackberry. unlock it and use it with a T-mobile SIM card with 3G speeds you should get your device from WIND or Mobilicity..
I know first hand it is not worth it. I unlocked an AT&T 9810 and used my T-mobile sim in the phone and was disappointed. You will be on 2G all the time constantly getting a weak signal and the phone will be painstakingly slow when doing anything involving the internet.
Either get an AT&T sim card or if you need to stay on T-mobile get a 4G card.
Otherwise its like putting a pinto's engine in a Ferrari.
You probably won't get LTE, you will get HSPA+ if it is a market that T-Mobile refarmed for 1900MHz HSPA.
I can confirm an unlocked att 9810 gets H+ on T-Mobile service in a refarmed area!! H+ works just as well as the T-Mobile LTE I get on my unlocked Rogers pentaband Lumia 920