Hello, Can you play games on GOG against other players online and or coop ?

That depends on the game. Once in a blue moon, sometimes, for some games, yes.

Generally speaking though, no you can't.

And for the few games where you can, multiplayer is generally not viable if it is limited to Galaxy-only multiplayer (Galaxy is GOG's client), because the population of players there is way too small and mostly non-existent for most games.

GOG is not really a viable multiplayer platform at all, in general.

If the game allows it and if you want to.

Yes, look at each game in the store to see whether it supports multiplayer features or not, and what types of multiplayer. In particular games that support crossplay will have a larger number of players in them potentially as this is basically cross-store multiplayer, so it brings in players from Steam or other storefronts for games that support the crossplay.

Also, there are games that support direct peer to peer multiplayer (I believe the Larian Studios games do?), which is decentralized, but this is not common in the game industry as a whole, yet nice when a game does support it. Some games may also support LAN multiplayer also, which can theoretically be played online using VPNs such as Hamachi between players.

Be sure to read each game's store page to see what features are supported for that specific game including multiplayer, and if you have questions about a specific game and it's multiplayer functionality it might be useful to ask about it in that game's specific forum here also.

Hope this helps.