The first two instances of the word “you” are plural and refer to the Jews to whom Paul is speaking.
Here the words “we” and “us” refers to Paul and Barnabas but not the crowd that was present. (See: rc://en/ta/man/translate/figs-exclusive)
Paul’s quotation is from the prophet Isaiah in the Old Testament. In the original passage, the word “I” refers to God and the word “you” is singular and refers to the Messiah. Here, Paul and Barnabas seem to be saying that the quotation also refers to their ministry.
This implies that God had commanded this be done. AT: “God commanded” (See: rc://en/ta/man/translate/figs-explicit)
This can be stated in active form. “Word of God” here is a synecdoche for “message from God.” AT: “that we speak the message from God to you first” or “that we speak the word of God to you first” (See: rc://en/ta/man/translate/figs-activepassive and rc://en/ta/man/translate/figs-synecdoche)
Their rejection of the word of God is spoken of as if it were something they pushed away. AT: “Since you reject the word of God”
“have shown that you are not worthy of eternal life” or “act as though you are not worthy of eternal life”
“Turn” is idiomatic for “change direction toward.” AT: “we will now change our direction toward the Gentiles” (See: rc://en/ta/man/translate/figs-idiom)
Here the truth about Jesus that Paul was preaching is spoken of as if it were a light that allowed people to see. (See: rc://en/ta/man/translate/figs-metonymy)
The abstract word “salvation” can be translated with the verb “to save.” The phrase “uttermost parts” refers to everywhere. AT: “tell people everywhere in the world that I want to save them” (See: rc://en/ta/man/translate/figs-abstractnouns)