Here the word "mouth" refers to the words that David spoke or wrote down. Alternate translation: "by the words of your servant, our father David" (See: [[rc://en/ta/man/translate/figs-metonymy]])
This is a rhetorical question that emphasizes the futility of opposing God. Alternate translation: "The Gentile nations should not have raged, and the peoples should not have imagined useless things." (See: [[rc://en/ta/man/translate/figs-rquestion]])
These "useless things" consist of plans to oppose God. Alternate translation: "the peoples imagine useless things against God" (See: [[rc://en/ta/man/translate/figs-explicit]])