There was a famine - When this happened we cannot tell; it appears to have been after the death of Abraham. Concerning the first famine, see Gen 12:10.
Abimelech - As we know not the time when the famine happened, so we cannot tell whether this was the same Abimelech, Phichol, etc., which are mentioned Gen 20:1, Gen 20:2, etc., or the sons or other descendants of these persons.