The church was established on Sabbath observance, yes Paul and Barnabas observed church on the Sabbath, and they admonished the early church to continue in this grace of Sabbath observance
Yes they met on the Sabbath, no it wasn't Sunday, yes they were new converts proselytes, yes this was the early Church
Merriam-Webster
Definition of proselyte
: a new convert (as to a faith or cause)
Acts 13:42-44KJV
42 And when the Jews were gone out of the synagogue, the Gentiles besought that these words might be preached to them the next sabbath.
43 Now when the congregation was broken up, many of the Jews and religious proselytes followed Paul and Barnabas: who, speaking to them, persuaded them to continue in the grace of God.
44 And the next sabbath day came almost the whole city together to hear the word of God.