REDUCTION GEARS, PULLEYS AND LEVERS

It is not possible to move 0.01mm because the driving motion is directly connected with the M12 screw rod.
in this case we added one more step down gear system (worm and worm wheel) with suitable ratio

Like I ask all my designers, "What, exactly, are you trying to do?"

The technical part of it is a given; you want 1 rev = 10 microns but with what kind of repeatability? How will you quantify that movement? What are the accuracy requirements?

and... again, what are you trying to do?

First of all, If you have an M12 rod ( fine (pitch 1.5 m or coarse (pitch 2 mm)) and a nut fixed to at your device
Let suppose is coarse, then when you rotate the red a revolution, the nut will move forward 2 mm.
If you have to move 0.01 mm, you must rotate: 1 rev ----- 2 mm
x rev -----0.01
0.005 rev (1/200 rev). If your lever has a longitude of 50 mm, you must to move 1.57 mm

A Practical inconvenience is that rod and nut, do not fix exactly, always you have some clearance, more than a 0.01 mm

did you check the differential screws ?
https://en.wikipedia.org/wiki/Differential_screw