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The church met to eat the Lord's Supper and to have meetings in which the saints were edified through use of the gifts of the Spirit. In the epistles, we see that this was done, or was to be done, through mutually edifying meetings in which the saints were to exhort one another. The scriptures were also to be read.
Originally the gifts were manifested in many places. They were manifested just walking down the streets, stopping, and healing, etc. Paul was bitten by a snake, he was ship wrecked and had a word of knowledge beforehand, etc. However, that is not the nature of your original question is it (Is the Sunday sermon Biblical?)? Paul TOLD the Corinthians that their "services" were not being conducted properly and for them to be changed.

PS: We use many terms to describe things in Scripture that cannot be found in the text (Trinity, Infralapsarianism, Sublapsarianism, etc)--but it does not mean they are the wrong terms. Communication is imperative and thus words of many sorts must be used.

Reformed and Always Reforming,