This is a personal letter from John to Gaius. All instances of "you" and "your" refer to Gaius and are singular. (See: [[rc://en/ta/man/translate/figs-you]])
This refers to John, the apostle and disciple of Jesus. He refers to himself as "elder" either because of his old age or because he is a leader in the church. The name of the author can be made explicit: "I, John the elder, am writing." (See: [[rc://en/ta/man/translate/figs-explicit]])
Walking on a path is a metaphor for how a person lives his life. AT: "you are living your life according to God's truth" (See: [[rc://en/ta/man/translate/figs-metaphor]])
John speaks of those he taught to believe in Jesus as though they were his children. This emphasizes his love and concern for them. It could also be that he himself led them to the Lord. AT: "my spiritual children" (See: [[rc://en/ta/man/translate/figs-metaphor]])