(Not sure if I posted in the right category because I do not yet know what fundamental analysis is, but figured its some kind of math - total Noob here, so please excuse if my question is stupid 
)
I’m assuming that the number of overall stocks being traded in the market for a company, remains constant. In any days, huge volume of stocks are being purchased and sold for a company. Lets assume some person X purchased 1 share some time ago, and now sold it to another person Y.
My questions are:
- Do the shares being traded in market [of any company] have a unique identifier so that it can be tracked ?
- Is it possible for a observer Z to see that this particular share was sold between X and Y and the prices at which it was transacted ? I can see the numbers in volumes, but can I know exactly which share was purchased/sold at what quantity ?
- If a normal trader cannot get this info, can an agent registered with SEBI or can get this info?
I am not interested in knowing personal information of traders, but opaque unique identifiers that can be associated with a share and a trader that I can study.
If you’re curious why I need this info, my answer is also the same - curiosity 
to study how many people purchased a share at what price and at the same time being able to track what happens to one single share as it gets transacted across traders over time.