1)
Why did Achish swear in the name of Hashem?
1.
Radak: All agreed that Hashem is the first cause [of the world]. He swore in His name because David believed in Him.
2)
Why did Achish say that the Sarnim object? All the officers objected!
1.
Malbim: He did not want to upset David that the officers distrust him. He said that the generals are jealous that he guards the king.