I have the Steam version so if GOG's version is completely different it doesn't apply but I doubt that.
1. Does it really need EAX? My onboard soundchip doesn`t support it. Afair from the boxed version it doesn`t need EAX, it`s optional, right?
No it doesn't need EAX but you only have stereo on Windows Vista and higher because of changes made in DX (read Microsoft's PC degrading strategy in favour of pushing their console).
If you want surround under Windows Vista and higher but you don't have a soundcard from Creative, you might want to try Indirect Sound
which gives you surround sound but still no EAX.
2. Does it work correctly under Win 7? I heard that the game has problems under Win 7 when it`s patched.
The game should work, I have read on several sources that the game does have framerate problems with certain keyboards and mice of Logitech's G-series, but I haven't encountered them myself as I don't have that hardware.