To sit at God’s “right hand” is an idiom that means that Christ will rule as God, with God’s authority. AT: "with God in ruling as King"(See: rc://en/ta/man/translate/figs-idiom).
This idiom means they proved that their message was true. AT: "showed that his message, which they were speaking, was true" (See: [[rc://en/ta/man/translate/figs-idiom]])