Why is Electrostatic Potential Energy positive when the charges are like? We know that in an atom charge of an electron at infinity is zero. As it approaches the nucleus it become more and more negatively charged.
We also know that E.P.E is positive when charges are like and negative when charges are opposite.
Well does it mean that as an electron approaches nucleus there is repulsion which causes the approaching electron to go away. As the electron go away it is getting closer to to infinity point because of which electron become less and less negatively charged. So the E.P.E is positive .Nucleus of atom is like earth and the electron are objects.The farther the object move from earth it has more Potential energy.
There is no way to know the actual potential energy of a system, we can only determine it relative to some predefined zero value.  In the case of electrostatic potential, zero potential energy is defined as the energy between charges when their separation is infinite.

The charge of the electron doesn't change in this scenario; it is always $1.6\times 10^{-19}\ C$.

When oppositely charged particles near one another, they lose potential energy (their energy becomes more negative.)  When particles with the same charge near one another, they gain potential energy.  The attractive force between oppositely charged particles does work as their separation decreases, and the repulsive force between similarly charged particles requires work to be done on them in order to move closer to one another (so potential energy goes up.)