In the case of an engine failure, a helicopter trades its potential energy (altitude) to kinetic energy by allowing the passing air (as it 'falls') to spin the rotors. This is the helicopter's equivalent of gliding, more or less. The condition is called auto-rotation. Gyros are always in a state of auto-rotation, so if the engine quits they simply begin trading potential energy for kinetic energy, which they're really good at.

Yes they can. There are no hydraulic assists between the stick and the the rotor head, or between pedals and rudder - straight mechanical linkage.

The only electric (or in some cases pneumatic) assist is the pitch trim. In event of failure that would usually stay in the same place, but in the worst case where it moves to one end of the spectrum you can absolutely control the aircraft against it (your arm just gets a bit tired after a while maintaining the pressure).

Yes. They're small enough to not need power-assisted controls.