1.How to calculate absolute potential at the surface of one of the plate having charge +q of a capacitor.

2. Why don't we take charge on both sides of the plate of a capacitor?

Generally, Charge resides on the surface of conductor (due to the presence of free electrons).

If equal but opposite charges are given to two plates which are next to each other, the charge comes to the facing surfaces (as only that configuration can make electric field zero inside the material of conductors) leaving the outer surfaces uncharged.

However, it can be seen easily - from the fact that electric field inside conductor is zero - that when the plates are given unequal charge the outer surfaces too shall have charge density.

The distribution of charge will be always such that electric field inside the material of the conductors is always zero.