Here the word "We" refers to the apostles, and not to the audience. (See: rc://en/ta/man/translate/figs-exclusive)
Peter spoke on behalf of all of the apostles when he said the following words.
"Raised up" here is an idiom for "caused to live again" AT: "The God of our fathers caused Jesus to live again" (See: rc://en/ta/man/translate/figs-idiom),
Here Peter uses the word "tree" to refer to the cross which was made out of wood. AT: "by hanging him on a cross" (See: rc://en/ta/man/translate/figs-metonymy)
The words "repentance" and "forgiveness" can be translated as verbs. AT: "give the people of Israel an opportunity to repent and have God forgive their sins" (See: rc://en/ta/man/translate/figs-abstractnouns)
The word "Israel" refers to the Jewish people. (See: rc://en/ta/man/translate/figs-metonymy)
"those who submit to God's authority"