How does a particle detect the presence of another? And also how does it know whether to attract or to repulse without even interacting with one another?
In the "field theory" model, each particle creates a "field" [Faraday's lines of force] (for example, an electric field) that extends from the particle out to infinity. Tthe particle that creates the field can be thought of as the "source of the force".
Then, a distant particle ["the target"] experiences forces due to the fields that it encounters at its position.
How does it differentiate between +vely and -vely charged particles? And know the exact force to be applied on the particle; not more, not less: just exact? is there something i am really missing out?
as robfy said, through the fields. their magnitude and direction convey the information of how much force to experience and in which direction depending on whether the particle experiencing them is negatively or positively charged.