No.1115
You could add a bit of starch to the dough. This way you don't have to press as much water out, since it acts as a binder and thickener.
No.1116
I don't squeeze the potatoes at all, just shred them straight into the frying pan. Tried the soaking thing but it was much harder to keep them from falling apart that way. You're really just squeezing off the water you've added when you soak them to remove the starch. (or people in america have some WAP (wet ass potatoes))
Some water does evaporate during cooking, but I can't imagine it being even close to half the weight, would be interesting to measure.