General Questions on a Carrier Unlocked ATT HTC M7

[charkswitlazers]

So I just bought a used black M7 on ebay - it was locked to att but is apparently unlocked to all GSM carriers.
I have a few questions...

1: If I root and flash a rom (or even do a factory OTA), will my phone become locked again? I am going to use it with T Mobile and can't risk it becoming re-locked to ATT...

2. I would assume that all of the ROMs I choose must be specific to the ATT model? or can I use ROMs for the factory unlocked verson?
I'm new to the whole unlocked thing, and I want to know as much as possible BEFORE i start tweaking my phone.... lol..

3. Will the phone fully work on T Mobile's LTE?? Does ATT use the same frequencies? (the seller did not know if it would work well with data)

any knowledgeable input is greatly appreciated

thanks!!