What do you reckon I'll be able to do after 12 ice-skating lessons?

After about 12 lessons, you'll probably have a good grip on all the basics. You'll go over things like falling down/getting up safely, forward marching, 2-foot glides, 1-foot glides, swizzles/gvines, basic stops, backward glides (one and two feet), backward "wiggles," backwards swizzles/gvines, 2-foot turns, pump circles, mohawks, probably crossovers (forward and backward) and maybe even 3-turns. Because of your ballet background, you'll probably progress quickly if you're coordinated. You will most likely cover all the very basics of forward and backward skating and depending on your progress with that, probably move onto a little more advanced things like 3-turns (a one foot turn done on each foot, forwards and backwards, on both blade edges -- inside and outside) and probably even a 2-foot spin! I think because of your background, you'll progress rapidly. :) Good luck!