Speaking together, the people quote a Psalm of David from the Old Testament.
Here the word "they" refers to the rest of the believers, but not to Peter and John.
The phrase "their own people" refers to the rest of the believers. AT: "went to the other believers" (See: rc://en/ta/man/translate/figs-explicit)
"Raised" here is an idiom for "increased the sound of their voices" AT: "They increased the sound of their speaking together to God" (See: rc://en/ta/man/translate/figs-idiom)
This means that the Holy Spirit caused David to speak or write down what God said.
Here the word "mouth" refers to the words that David spoke or wrote down. AT: "by the words of your servant, our father David" (See: rc://en/ta/man/translate/figs-metonymy)
Here "father" refers to "ancestor/"
This is a rhetorical question that emphasizes the futility of opposing God. AT: "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. AT: "the peoples imagine useless things against God" (See: rc://en/ta/man/translate/figs-explicit)
"people groups" or "tribes"