Paul wrote the same thing Moses wrote (see: Deuteronomy 19:15). This was a part of the Law of Moses. Someone could only be judged if more than one person saw them do something wrong. They needed two or more witnesses.
Scholars think to be “alive by God’s power” not only indicated that Jesus was resurrected, but that he continues to live and rules everything because he is God. They think Paul lived by the power of God in his life and that he would go to the church in Corinth in the power of God. That is, God gave Paul permission to lead the Christians in Corinth.
Paul wanted the Corinthians to examine the things they did and to test the genuineness of their faith. That is, Paul wanted the Christians in Corinth to live according to what they said they believed.
Paul said, “we are not able to do anything against the truth.” Some scholars think that the apostles were actually unable to act against the truth. This is something God did. Other scholars think that even if the apostles spoke in a wrong way, it would not change the truth of the gospel.
To build up meant to encourage the Christians to live in a way that honored Jesus. To tear down was to discourage Christians from living in a way that honored Jesus. Paul always served to “build up”(οἰκοδομή/g3619) the Corinthians. (see: 2 Corinthians 10:8).
Paul encouraged the Christians to work for “restoration”(καταρτίζω/g2675). The Corinthians must allow God’s ways to work in them, that is, to help them to live in a way that honors God. Perhaps Paul’s greatest concern was to see the Christians in Corinth joined together and working together to serve God.
In ancient Israel, people usually only kissed their family members. By kissing one another, the Christians signaled that they were members of the family of God. The “holy kiss” was probably a kiss on the cheek.
Paul wrote about experiencing the “fellowship”(κοινωνία/g2842) of the Holy Spirit. This is doing the things the Holy Spirit wants them to do and to be joined with the Holy Spirit in some way. He wanted Christians to want to do things that honored God, just as the Holy Spirit honors God the Father (see: Philippians 2:1-4).