First: Vader left the Death Star because its commanding officer refused to launch the station's fighters. Vader took his own personal wingmen in a valiant attempt to save the Death Star.

Second: Vader's TIE fighter is not lightly armored. It contains a sheild generator and a hyperdrive.

Third: The large Rebel fleet doesn't exist. The fleet remaining at the end of the battle and in any position to stop Vader consited of only Luke, Han, and a couple of other (damaged) fighters.

Fourth: He didn't fly away. When Han shot the TIE fighter beside him, it crashed in to him. The sheild generator protected him, but he lost control of his ship and spun away.

Fifth: It wasn't a rout. The Rebels barely managed to destroy the Death Star, and many Imperial ships were quickly dispatched to Yavin. They didn't have time for a prolonged search for a small ship that posed no immediate threat.

Sixth: Of the Imperials, only Vader and the Emperor know Like is Vader's son, and the Emperor trusts Vader.