What does Paul list as the core components of a church service? Why are these important and central?

These were the essentials in the first century church: the communion supper was observed (Acts 20:7; 1 Corinthians 11:25–26), prayers were offered up (1 Corinthians 14:15–16), songs were sung to the glory of God (Ephesians 5:19), a collection or offering was taken (1 Corinthians 16:2), and the Scriptures were read, preached and taught (Acts 20:7; Colossians 4:16; 2 Timothy 4:2).

I do not think he listed all in one passage, but he did let the churches know throughout his letters what they needed to do to hold a worship service. (the biblical passages you see, Acts was not written by Paul but it narrates his part of his life and ministry from chapters 9 thru 28).

They are important because besides praising God passionately, their faith was shared with others and more people were been converted to Christianity, so they needed to be nurtured spiritually to grow in their faith and know God better with the help of the church leaders through the Scripture.

Hope it helps! If you have another question, comment this answer. I’d be more than glad to help.