Verse 35 is the end of the part of the story that began in [Matthew 8:1](../08/01.md) about Jesus' healing ministry in Galilee. (See: [[rc://en/ta/man/translate/writing-endofstory]])
The word "all" is an exaggeration to emphasize how very many cities Jesus went to. He did not necessarily go to every one of them. Alternate translation: "many of the cities" (See: [[rc://en/ta/man/translate/figs-hyperbole]])
Here "kingdom" refers to God's rule as king. See how you translated this in [Matthew 4:23](../04/23.md). Alternate translation: "preaching the good news that God will show himself as king" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])
"every disease and every sickness." The words "disease" and "sickness" are closely related but should be translated as two different words if possible. "Disease" is what causes a person to be sick. "Sickness" is the physical weakness or affliction that results from having a disease.