Probable meanings are 1) the words "reasoning" and "persuading" are a hendiadys that means "arguing persuasively" or 2) the words describe two separate activities, "giving them reasons to believe" and "convincing them" (see how you translated "reasoning" in [Acts 17:2](../17/02.md)). (See: [[rc://en/ta/man/translate/figs-hendiadys]])
Here "kingdom" stands for God's rule as king. Alternate translation: "about God's rule as king" or "about how God would show himself as king" (See: [[rc://en/ta/man/translate/figs-metonymy]])