To "open the mind" is an idiom that means to enable someone to understand. AT: "Then he enabled them to understand the scriptures" (See: [[rc://en/ta/man/translate/figs-idiom]])
The Jews counted any portion of a day as a day. Therefore, the day Jesus was raised was the "third day" because it followed the day of his burial and the Sabbath day. See how you translated this in [Luke 24:7](./06.md). (See: [[rc://en/ta/man/translate/translate-ordinal]])
This can be stated in active form. AT: "Followers of the Christ should preach to people in all the nations that they need to repent and that they need God to forgive their sins through Jesus" (See: [[rc://en/ta/man/translate/figs-activepassive]])