Question

What exactly does Nestor tell Telemachus about the War and the return home? Why does he dwell upon the fate of Agamemnon, killed by Aegisthus, the lover of Clytemnestra?

Answer 1

About the war and return home, Nestor tells Telemachus that the Greeks sacked Troy and then prepared to sail away.

Secondly, this is because Telemachus is supposed to draws inspiration from it. Aegisthus killed Agamemnon and is eventually killed by Orestes, Agamemnon's son as an act of vengeance.