Balance and flexibility

I previously made a post about wanting to start figure skating. I felt motivated to actually try it out because of the encouraging and informative comments I got. I now have had my two first very basic trainings. The second training was about the one foot glide. I’m still not too comfortable on the ice so I was having a hard time. Is there anything I can do to increase my balance on one foot on the ice? Or is this something that just takes time and getting used to? There’s a lot of things that intrigue me about figure skating and I’m going to continue doing it. Since I like to believe flexibility is a big part of it, I was wondering what exercises would be recommended. So what daily exercises should I do to become more flexible? As for now I’m as flexible as a tree and I’ve never had to work on my flexibility before.