mamindz:
it seems that I can acquire my desired flow rate with a 1 ml syringe which has 4.69 mm inner diameter.
Flow Rate=0.001254.69^2pi*3600=310.8 ul/h. It is not 100 ul/h but that's precise enough.
I don't follow the calculation.
If the diameter is 4.69mm then the piston area is 4.69 * 4.69 / 4 * Pi = 17.276mm2
And if the stepper were to advance the piston by 0.00125mm then the change in volume would be 17.276 * 0.00125 = 0.0216 mm3. I think that is about 21 µL and if so it would require about 5 steps to dispense 100µL
EDIT - just realised 1mm3 = 1µL and I had unncessarily divided by 1000 so it should have been about 5000 steps for 100µL.
(By the way I would not be surprised if I have got my maths wrong 
)
-Would be there any problem in using VEXTA PK243A1-SG18-C4 Motor with Arduino Uno?
That stepper motor has an 18:1 gear reduction - which may be very beneficial for your project but you will need to consider carefully whether backlash in the gearbox would cause a problem with precision.
In my calculations I had been assuming a stepper motor without a gearbox.
...R
PS ... to get repeatable movements of 0.00125mm you will need a VERY high quality mechanical support system.