I`m sorry for the mixup, but the whole thing is a mess. The reality of flying in the US right now is that if you are in the country legaly you can do the flight training.(except over 12500lbs)
Nobody asks any Q and even the examiners dont care what kind of visa you are on as long as you pay the fee. Working as a CFI is another story....
A friend of mine got a F/O job with Mesa just before New Year and he is not a citizen, just a green card holder. If you wanna call him I can get you the number trough PM. And he`ll explain first hand how things work.