Weirdly, I definitely found my skiing was much improved by my skating!
It's hard to know what you don't know, of course, but me and Astrid, who as far as I could tell were the more experienced figure skaters, didn't seem to be getting the hang of anything any faster than the others, and slower than some.
ETA I think the difference is that in figure skating, the push comes from your skating leg. In tour skating, the push comes from the free leg, sideways not forwards, and the skating leg just glides (usually a great way to catch your toepick and fall over). I wish I'd worked that out three days ago!
Re: Everything sounds great except the overreis
It's hard to know what you don't know, of course, but me and Astrid, who as far as I could tell were the more experienced figure skaters, didn't seem to be getting the hang of anything any faster than the others, and slower than some.
ETA I think the difference is that in figure skating, the push comes from your skating leg. In tour skating, the push comes from the free leg, sideways not forwards, and the skating leg just glides (usually a great way to catch your toepick and fall over). I wish I'd worked that out three days ago!