I saw someone do some tricks with a toy helicopter where he would turn it upside down for a while and it would still stay in the air. I thought it should have crash or at least not fly for very long in that position, but I was wrong. Is it possible for the helicopter to have change its propellers turing direction so fast (in less than a second) so it could still fly upside down?
The helicopter you saw must have had collective pitch control, as many do. This allows it to reverse the pitch of its blades almost instantaneously and fly upside down. It does NOT reverse the direction of rotation of it's blades.
Yes all it is doing is changing the angle the blades sit at to such a degree that they effectively push up instead of down. Then it can fly upside down as long as you want.