In other words, what happens to vertical speed and rpms in vertical autorotation if I change the pitch of the blades of the gyro I use to fly...?
Unless I am misinterpreting your question, if you add pitch [pulling collective in a helicopter] your RRPM [rotor RPM] will decrease, as it is being used to accelerate air down decent, if in a vertical decent the aerodynamics are screwy. Now if you have some forward speed increase Pitch trades RRPM for lowering vertical speed. Decreasing Pitch, allows you to trade altitude for RRPM giving you higher VS and higher RRPM.
For what it's worth, when conducting routine maintenance test flying, Autorotation is performed in order to check the auto rpm. Helicopter manufacturers specify an rpm range for autorotation. If the rpm is too high the pitch change links (pcl) are adjusted to increase collective blade pitch. If the auto rpm is too slow, pcls are adjusted to decrease collective pitch. most pilots and flight departments prefer the rpm to be at the high end of the range, allowing additional rotor energy options for the pilot. This technique must not be overdone else collective authority in the flare/touchdown will be adversely limited.