Question

Is calculating the electric field on a dipole using Coulombs law the same thing as calculating the electric field of each charge individually and then adding them by superposition?

Answer 1

yes, if you want to calculate the electric field for a dipole you can first calcule for the positive charge and then for the negative charge.
the you have:
\[E(r) = E(r _{1}) + E(r _{2)}\]

Answer 2

exactly as electric field is the force per unit test charge!!!! you can find the force experienced by the test charge divided by that charge!!! in this way you can find electric field then use superpossition principle