A) In ERAS, you will look like a AMG, because that's exactly what you are: An American Medical Graduate, i.e. a graduate from an LCME-accredited school. AMG is based on where you were taught medicine, not the color of your passport.
B) If you have a permanent residency and work permit, there's no need for programs to be concerned about visa issues, so I see absolutely no reason to even bring that up.
There's a few creveats to the above. E.g., you cannot directly receive NIH research funding, unless you are a US citizen or green card holder. I -think- the same applies to a few Federal residency programs (like NCI etc.). And they'll spell out such special requirements. Other than that, you'll apply just like your classmates, and have no need to concern yourself with ECFMG, IMG/FMG status, and all that other nonsense.