# Potential energy of charge gradually moved to infinity away from another charge

(a) Is correct! The potential energy $U$ for equal but opposite charges is negative $$U=\frac{-|Q||Q|}{4\pi\epsilon_0 r}$$ Thus $U$ increases (becomes less negative) when you move one charge away from the other.
(b) When the distance between the charges goes to infinity $r → ∞$ $U → 0$. This is a conventional choice. You could add any arbitrary constant $U_0$ to the potential energy $U$.