I am not an instructor but I have suffered too from hopping drills (to NZRide this is done in traverse across the hill then you turn normally and hop back the other way). The purpose as it was explained to me is to promote good body position over the board. If your body is not in the right alignment over the board you fall. Which is probably what is happening to the OP.
Yeah I think NZRide might have just misread that a little. He's not doing the hops into a turn, I assume from his description he's doing a very typical exercise where you get on one edge, do a few hops as you traverse to get you used to pressuring and balancing on that edge, then turning like normal and doing it the other way.
As far as the OP's questions go:
1) Is it normal to feel more comfortable on your toe edge
Yep. Your toe edge is always more stable and balanced vs. your heel edge. That's normal so don't worry about it.
2) How do you balance on your heel edge
Again it's about flexing your ankles/knees etc, but the difference with heel edge is you have to get used to bending correctly.
The mistake you're probably making now is you're trying to engage your heel edge by just leaning backwards onto it, which isn't that stable.
You want to get used to basically squatting (many instructors call it sitting on the toilet) as your riding position when engaging your heel edge, that gives you the balance to engage your heel edge better and more balanced.
The tricky part to pay attention here is you want to squat and stick your butt out, but you also want to avoid bending at the waist as much as possible. So your knees bend, your butt goes out and you engage that heel edge, but your upper body stays upright as much as possible. It'll feel a little awkward at first, but you'll get more used to it as you go.