Unlocked T-mobile iphone 5 on At&t network?

Hi
I was wondering if tmobile iphone 5 work on att network or not. Here are my questions:

1. Do i need to get it unlocked to work on att network?
2. If I do get it unlocked, does 3g (HSPA+) work on att network?

I heard that tmobile uses 1700/2100 while att uses 850/1900 for 3g but I also heard that tmobile uses 1900 for edge speed so device should support 1900 mhz. Does anyone know what frequency tmobile iphone 5 support? Will it work flawlessly on att 3g?

Thanks

edit: I also heard that Tmobile iphone 5 is basically same as att iphone 5 but just tweaked little bit. I guess that means it supports att 3g frequencies?