1)
Why did Sha'ul ask David "who is your father"?
1.
Malbim: Sha'ul resolved to give his daughter to him, like he had promised, so he asked about the lineage and standing of David's father.
2)
Why did David say that his father is "Avdecha Yishai Beis ha'Lachmi"?
1.
Radak: Beis ha'Lachmi means that he is from Beis Lechem, and also, he was an Ish MiLChaMah - I am a Gibor's son!
2.
Malbim: David had no intent to ask for reward for his act. He did not realize that Sha'ul asks about Yishai's lineage and standing for the sake of the marriage. He said, the attribute of [me and] my father is that he is the king's servant; he obeys him.