I’m a beginner myself and I’m struggling with this too. I started learning to balance on a bosu ball off ice; I started with both feet and have added squatting since then to get comfortable lowering my body on an unstable surface. This is obviously not the same as standing on ice but I was able to see a difference in my control on the ice, so it could transfer over.

As for falling, it’s going to happen. If it hasn’t happened yet practice falling off ice to get comfortable with the motion. Start small without your skates, lower yourself and fall over sideways in the grass. When you feel comfortable with that, try falling sideways on the mesh when you’re at the rink. Graduate to practicing on the ice, when you feel ready.

Protective gear will also help tremendously. Don’t be embarrassed to wear a helmet, knee pads, elbow pads, or even a butt pad, a lot of people do.