"he seriously told them and begged them." Here the words "testified" and "urged" share similar meanings and emphasize that Peter urged them strongly to respond to what he was saying. Alternate translation: "he strongly urged them" (See: [[rc://en/ta/man/translate/figs-doublet]])
The implication is that God will punish "this wicked generation." Alternate translation: "Be saved from the punishment that these wicked people will suffer" (See: [[rc://en/ta/man/translate/figs-explicit]])
Many translations understand these words as a call to action, "Save yourselves." That is, he is telling them that they have to act, and if they repent and have the apostles baptize them ([Acts 2:38](./38.md)) God will save them. He is not saying that they can save themselves by their own actions.