Here "raised up" is an idiom. Alternate translation: "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. Alternate translation: "by hanging him on a cross" (See: [[rc://en/ta/man/translate/figs-metonymy]])