What is the meaning of "Ho'el"?
Rashi: Desire. Radak - this is like "va'Yo'el Moshe" (Shemos 2:21), "Ho'el Na v'Lin" (Shoftim 19:6), "Hinei Na Ho'alti" (Bereishis 18:27, 31).
Radak citing Targum Yonasan: Begin. This is like Targum Onkelos of the first "Hinei Na Ho'alti", i.e. Sharisi. 1
In our texts, Yonason translates so in both verses, but Onkelos translates both of them 'Asgisi' (I increased).
What is the meaning of "Lihyos l'Olam Lefanecha"?
Radak: They will always serve You. Malbim - David needed to pray only about this. Hashem's promises are always fulfilled if the recipients are worthy. "You spoke" - there is no change from Your side.
What is "Beis Avdecha l'Olam"?
Radak: David refers to himself, like the other occurrences of the word "Avdecha"(in his words here).
Radak citing Targum Yonasan: The houses of Your slaves, i.e. Tzadikim, forever.