Back in 2015 when I installed GIMP it wouldn't work scheit. I checked around and was told I should load PuTTy and Ghostscript. I am on the latest GIMP on a Win7 box, soon to be replaced with a Win10 box. Are those two programs needed any more?
I don't remember that PuTTY was ever a requirement. Aren't you confusing with Python? Python is embedded in the Windows versions since Gimp 2.8. Note sure about GhostScript, but I think GhostScript is no longer needed too.
A separate ghostscript installation not required in Gimp 2.10
.ps and .eps should open ok
.ai - depends where it comes from. Some open some fail
.wmf should open but the file import plugin is broken.