Transistor driving LED
My question is how to precisely express this voltage drops in a
  transistor or LED in order to manipulate such a small current.


The volt drops in the transistor and LED are subject to temperature variations and are also not constant between one device and the next. You won't get precision and control trying to use the hFE (current gain) of a BJT; to get precision you need feedback.

So, if you want precision, I would consider using a driver with an op-amp like this: -



The op-amp ensures that the current through the sense resistor produces a voltage across it that matches Vin hence, the current through the LED is held reasonably constant. This is feedback and it overcomes the temperature dependent variations in both the LED and BJT.

A slightly simpler circuit that drives the LED directly from the op-amp is this: -



But you need to use an op-amp that can drive the LED current and this limits the devices that are available should current be in excess of 20 mA.


  i would like to know how to calculate Vbe which depends on current. it
  could be 0.6 or 0.7 according to a datasheet. but what it exactly
  because 0.001 Vbe will affect the LEDS brightness if lets say Hfe is
  150


It depends on: -


Base current
Temperature
Variations between one device and the next


It has an exponential formula if you are interested: -



All three above are generally referred to as the Ebers-Moll equations and \$V_T\$ in the denominator of the exponential is the temperature dependency factor. \$I_S\$ is the reverse saturation current and this will vary between one BJT and the next.