Let's evaluate each statement:

1. Gauss's law $\oint \overrightarrow{E}·d\overrightarrow{A}=\frac{q_{enc}}{{ϵ}_0}$ is fundamental and independent of the $r^{-2.5}$ dependence. It remains valid for any field.

2. For two like charges (same sign), the electric field can be zero on the line joining them, but only if they are unequal. For two equal like charges, the field is never zero between them. This statement is not always correct.

3. Gauss's law is not useful for a dipole because the net enclosed charge is zero, giving no information about the non-uniform field distribution.

4. The work done by an external force is $W=q(V_B-V_A)$. For a unit positive charge (q=1), this is indeed $(V_B-V_A)$.

Final Answer: Only statements 1 and 4 are correct.