Yes and yes.
A certification requirement of helicopters with powered controls is that they have a manual reversion so that control can be maintained in the event of a power failure. However, the controls can be really heavy with no power and accidents have occurred when hydraulics have failed at critical moments or pilots have lifted off with hydraulics off and have been caught by suprise with the effort needed to maintain control.
The control inputs during autorotation are the same. For any given glide, or flare, the lift required is the same powered or unpowered. Lift is proportional to the speed of the blades, which is independent of powered or unpowered, and the angle of attack.
During autorotation, the energy (power) going into the rotors is derived from the airflow coming up through the disc. In this sense, an autorotation is still powered but the power comes from the airflow rather than the engine.
During autorotation, since the airflow is from below, rather than above, the pitch required is lower for the same angle of attack to generate the same amount of lift. So, the swashplate is lower in autorotation but lowering collective still decreases lift and raising it increases lift. The primary difference is that rather than controlling lift and power, the collective controls rotor speed since increasing pitch increases the angle of attack which increases lift and therefore increases drag, slowing down the rotor. Lowering the collective has the opposite affect.
The cyclic control is the same in all respects (you tilt the rotor thrust in the direction you want to go) since it increases, or decreases the pitch, and therefore the angle of attack, cyclically. The movement of the swashplate about the X and Y axis is independent of the position of the swashplate in the Z axis.
The pedals work in the same way too.
In summary, the only difference in the controls is the vertical position of the swashplate.