In this book, unless otherwise noted, the word "our" refers to Paul and Timothy (the one to whom this letter is written), as well as to all believers. (See: [[rc://en/ta/man/translate/figs-inclusive]])
Your language may have a particular way of introducing the author of a letter. Also, immediately after introducing the author, you may need to tell to whom the letter is written, as in the UDB.
"because of God's will" or "because God wanted it." Paul became an apostle because God wanted him to be an apostle and not because a human being chose him.
Possible meanings are 1) "for the purpose of." This means that God appointed Paul to tell others about God's promise of life in Jesus or 2) "in keeping with." This means that just as God promises that Jesus gives life, he has made Paul an apostle.
Paul speaks of "the life" as if it were an object inside of Jesus. This refers to the life people receive as a result of belonging to Christ Jesus. AT: "of the life that we receive as a result of belonging to Christ Jesus" (See: [[rc://en/ta/man/translate/figs-metaphor]])
"dear child" or "child whom I love. Here "child" is a term of great love and approval. It is also likely that Timothy was converted to Christ by Paul, and so this is why Paul considered him like his own child. AT: "who is like my beloved child" (See: [[rc://en/ta/man/translate/figs-metaphor]])
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