Romans 1:8-9 — First, I thank my God through Jesus Christ for you all, that your faith is spoken of throughout the whole world. For God is my witness, whom I serve with my spirit in the gospel of His Son, that without ceasing I make mention of you always in my prayers.
Through Jesus Christ — the only way to God in prayer as in anything else. Here Paul is emphasizing His incarnation, death and resurrection as the basis for our thanksgiving.
The whole world — everywhere that Paul went, he met people who were talking about the Romans’ faith.
God is my witness — Paul was often perceived as cold, but his love was sincere.
Serve = voluntary work, different from and in addition to the slavery of Romans 1:1.
My spirit — Paul is referring here to his new life in Christ, not the Holy Spirit.
Mention = recurring remembrance
Always in my prayers — should be connected to verse 10 — Always in my prayers making requests …