To answer the question about pitch in hover, lift of an airfoil, like the main blades, is related to airspeed and angle of attack. When we say "pitch angle" we are roughly referring to the angle of attack of the blades. If you have zero angle of attack, you will have zero lift, no matter the airspeed (rpm). This should be pretty obvious to any kid who has ever held his or her hand out the window of a moving car.
So if you set zero pitch, you will drop out of the sky because you are generating no lift.

And technically speaking I think most of the helicopters we will encounter are actually not dynamically unstable, but rather "neutrally stable" or astable. This is the idea that I was trying to convey with the sheet-of-glass analogy. A dynamically unstable analogy would be like balancing a marble on top of a bowling ball. Dynamically unstable aircraft need computer assistance to be flown by human beings.
Most fixed-wing aircraft are positively stable, they return to a trimmed attitude and require force on the controls to deviate from that attitude. Acrobatic airplanes, and helicopters, are designed to be neutrally stable, hence they keep doing whatever they are doing until something changes it, like a control input or a gust of turbulence. They require very little force on the controls to change attitude, and will not spontaneously return to a trimmed attitude, but will not "diverge" like a truly unstable aircraft will.