a) is there a gearbox involved or are you looking directly at stepper shaft
I notice the change by examining the output of the 3Dprinter, so yes, there is a gearbox involved.
However, its just a simple one. One drive gear mounted on a stepper motor inside a drive block to grab and push filaments.
(Note that, it is designed to move backward a tiny bit when it stop, where the amount can be adjusted. I am sure it is configured to just stop and hold.)
b) how must does it move by (part of 1 step or 1 complete step)
Probably part of 1 step , but I'm not sure about it.
c) do you keep the coils energised when stopped
Yes, the coils are energized, burning hot.
f) how many coils are used
I'm not sure about it.
g) and finally the model number of the stepper motor
Nema 17 Stepper Motor, http://store.makerbot.com/nema-17-stepper-motor.html
By the way, what is the different between an ordinary stepper motor and a Hybrid Stepper Motor?