I know that the GOG version will be DRM-free, but I have heard that the Steam version is also DRM-free: is this true?
Yes. Steam is only used as a download and patch platform, not for DRM. The game is DRM free.
[*]The Steam version presumably comes with Achievements that won't be available on GOG, correct? Not a big deal, but something to factor in.
Steam version has some achievements, yes. GOG might have something similar with GOG Galaxy.
[*]What would be a big deal is if the GOG version isn't compatible with original user-made content. I know that the Steam version uses Steam Workshop. Will there be a problem getting content released through Workshop into the Steam version?
Both versions should be essentially the same. Both are DRM free and can run without their respective platforms present. So it stands to reason both can use the same mods regardless of the mod's origin.
The engine toolkit can save mods standalone, so you can always load them like that.
[*]Also of great importance: will GOG and Steam users be able to play online with one another? And what's this whole GOG Galaxy thing about?
Yes, in theory at least. Larian has been working with GOG to integrate the game with GOG Galaxy, and GOG Galaxy is supposed to play nice with Steam users, for this game at least.
[*]What about future patches? Should we expect one version to be patched later than another?
I am guessing Steam will get updates pretty quickly, but I don't see why GOG would fall behind. They should be able to use the same game files for both platforms, as far as I know.