"a woman who was from that region and who belonged to the group of people called Canaanites came." The country of Canaan no longer existed by this time. She was a part of a people group that lived near the cities of Tyre and Sidon.
This phrase implies that she is requesting that Jesus heal her daughter. AT: "Have mercy and heal my daughter" (See: [[rc://en/ta/man/translate/figs-explicit]])
Jesus was not David's literal son, so this may be translated as "Descendant of David." However, "Son of David" is also a title for the Messiah, and the woman may have been calling Jesus by this title.
This can be stated in active form. AT: "A demon is controlling my daughter terribly" or "A demon is tormenting my daughter severely" (See: [[rc://en/ta/man/translate/figs-activepassive]])