False. Phoenix Jackson, the hero of the story, doesn't search for her family. She is a very old lady who is looking for a medicine for her grandson. She is going to the city on foot, which is a long and tiresome journey, and the story describes just one of these frequent journeys.
I'm not familiar with the text but I can infer that East Egg homes are flimsily constructed while West Egg homes are more durable and made eof quality material.