"He is the One heaven must welcome." Peter speaks of heaven as if it were a person who welcomes Jesus into his home. (See: [[rc://en/ta/man/translate/figs-personification]])
When the prophets spoke long ago, it was as if God himself was speaking because he told them what to say. AT: "about which things God spoke long ago by telling his holy prophets to speak about them"
Here the word "mouth" refers to the words that the prophets spoke and wrote down. AT: "the words of his holy prophets" (See: [[rc://en/ta/man/translate/figs-metonymy]])