Mostly what the title says. I'm having spotty internet, I got in the game, tried to keep my playthrough and found that the "load" option was greyed out and I could only start a new game.

Then I found out that somehow Galaxy wasn't connected. Is this an intented feature? Is my character locked to an internet connection?

A late answer for you and/or those looking this up in the future. Hellpoint has online saves and offline saves which can only be loaded in the resp. mode. See these posts:

https://www.gog.com/forum/hellpoint/hows_does_the_multiplayer_work/post5

https://www.gog.com/forum/hellpoint/save_types/page1