Rashi: David says so about himself; he was already anointed. Radak - they think to kill me, so I will not have kingship. They will perish, and the one who is proper to he king will rejoice in Hashem!

Rashi: When they will see that You will save me, all who cling to You and swear in Your name will be praised and glorified.

Radak: Everyone proper to swear in Your name, i.e. a Yar'ei Elokim and Ish Emes [will be praised].

Malbim #1: All servants of the king swear to him in Hashem's name that they will not rebel against him. Also David's men swore to him when they joined to him.

Malbim #2: All who swear in David's name; it was the custom to swear in the king's name, like "Chai Pharaoh" (Bereishis 42:15). They will boast, saying that even if David is expelled (refer to 63:11:1:3), the king will rejoice in Hashem, for He will save him from all his afflictions.

Rashi: Will be closed. This is like "va'Yisachru Mayenos Tehom" (Bereishis 8:2). Radak - because their mouths say Hashem's name for Sheker, their mouths will be closed and muted. This was said about Sha'ul, who swore in the name of Hashem that he will not kill David - "va'Yishava Sha'ul Chai Hashem Im Yumas" (Shmuel I, 19:6), and afterwards he chased him several times to kill him.