Whose youth was it?
Rashi: It was Avigayil's.
Why did he call them Mal'achim?
Malbim: This refers to a messenger on an honorable mission.
What is the meaning of "Levarech"?
Radak: It is to greet with Shalom, like "Ki Simtza Ish Lo Sevarchenu" (Melachim 2 4:29), "va'Yevarech Yakov Es Pharaoh" (Bereishis 47:7).
What is the meaning of "va'Ya'at"?
Rashi (from Midrash Shmuel 23:11): He verbally cast them away, like one makes a bird fly away. 1
Radak: He scolded them. The root is Ayit (refer to 25:14:4:1*), for there is a Kamatz under the Yud. He made them flee via bad words.
Radak citing Targum Yonasan: He abhorred them.
Rashi: This is from the root Ayit (Bereishis 15:11; it is the name of a bird).