"in the presence of God, who causes all things to live." It is implied that Paul as asking God to be his witness. AT: "with God, who causes all things to live, as my witness" (See: [[rc://en/ta/man/translate/figs-explicit]])
"in the presence of Christ Jesus, who spoke ... Pilate." It is implied that Paul as asking Jesus to be his witness. AT: "with Christ Jesus, who spoke ... Pilate, as my witness" (See: [[rc://en/ta/man/translate/figs-explicit]])
The word "spot" is a metaphor for moral fault. Possible meanings are 1) Jesus will not find fault with Timothy or blame him for doing wrong or 2) other people will not find fault with Timothy or blame him for doing wrong. (See: [[:en:ta:vol1:translate:figs-metaphor]])