Shambhala: Edit: Ok, the saving problem was just me being stupid, so that's not an issue anymore (I wish I could edit the title).
Actually, the title is what brought me to this thread. I was being stupid in probably the same way. Since the thread didn't help, I turned to GOG support and got my answer there.
Just in case anyone else is reading this because they don't see Save or Load buttons (they're blank), here's the trick: stop looking for the buttons and just type in the name of a game you want to save. Once you get something typed in, the Save and Load buttons will magically show up.
I had been playing MOM for a long time, but I got confused when I updated the game and then reinstalled it. As long as you have any past game saved, the Save and Load buttons continue to show up. I was so used to seeing them that I forgot they don't show up when the game is brand-new.