That's true, but irrelevant to the case of a moving treadmill. Friction is obviously important, which is exactly why planes have wheels, but rolling friction is such a minimal component of the hindrance to lift-off. Although rolling friction may increase as wheel rotation speed increases, it will still be a very minimal backward force compared to things like wind resistance.
No, it won't, actually, and that's the entire point. Rolling friction is constant regardless of speed. And a small constant at that. That would, in fact, be the reason why wheels are so awesome.
A sea plane first gets up on the step before it can take off. It has to hydroplane on the surface of the water first. Until it gets up out of the water it can't take off.
Technically it doesn't; it's merely that due to the properties of air and water, lift has an easier time raising the plane to hydrofoil than lifting it out of the water entirely. Same principal, just different critical speeds. If the plane managed to reach the liftoff speed before it was fully out the water it would take off immediately, but that doesn't happen in a practical situtation.