1)
What do we learn from "Nishbati va'Akayemah Lishmor Mishpetei Tzidkecha"?
1.
Chagigah 10a: This is a source to permit vows. (Rashi 10a - "va'Akayemah" implies that if he did not want to fulfill, they could permit his vow.)
2.
Nedarim 8a: This shows that one may swear to fulfill Mitzvos. (Tosfos 8a - even though the Shevu'ah of Sinai already obligates him, he may take a Shevu'ah to arouse himself to fulfill. (Radak - David did so.) Alternatively, he swore about a matter that he was not obligated in, e.g. to learn a particular matter today.
3.
Malbim: I accepted with a Shevu'ah, and I will fulfill, to judge the nation righteously, according to the Torah's laws.
