Is it possible to quantify/measure the effect of certain medication on our neurotransmitters and hormones? Is it possible to display the effect of taking for example Prozac on level of Serotonin and other neurotransmitters/hormones in the body? 

More generally speaking s is it possible to say: taking 1mg of medication A increases hormones B and C within 3 months by 2 units for the majority of people? or perhaps not this accurate but by some accuracy?

or taking food A, increases hormones C and D?

In other words is it possible to quantify the effect of any drug/food to the body?
Yes it is possible, but it is difficult. The way it would be done currently is to insert a needle into the base of your spinal cord to measure the concentration of a metabolite of serotonin, 5-HIAA, in the fluid surrounding your brain.

It is also possible to measure levels of this metabolite in saliva, urine, or in the bloodstream, but these measures would not necessarily represent the levels of serotonin in your central nervous system (brain). This is because serotonin plays a role in other (non-brain) bodily functions, and serotonin can not cross the blood-brain barrier. In other words, only serotonin that has been produced in the brain can be used by the brain.