1) Sadly, I don't know. "Stable" is sadly a stretch because of LGM which is unstable. But ENIGMA itself should run on Linux, it's just that I only try it on Windows.
2) Out-of-the-box, probably no. GM compatibility is not a goal anymore, so we don't strive for it. But the required changes are usually quite small. ENIGMA is planned to be less and less compatible with GM in future, so if good compatibility is essential to you, then you might reconsider using ENIGMA.
3) No. It is not really developed as far as I know.
4) Yes.
Here and
here are examples on how this can be done.
5) Not much. EDL (the scripting language in ENIGMA) is quite similar to GML, so that should be okay. IDE is also quite similar. You can switch platforms or specific systems in the ENIGMA settings window. I suggest choosing GL3.3 for graphical rendering and save projects in egm.