Was her mom not the only adult in her family at that time?
Page 24: "Minori's dad will probably be mad at me..."
They'd probably have moved into foster care if there were no adults left in the family, right? No way an elementary schooler would be left to look after two younger siblings on her own. Maybe the dad gets home from work too late to cook for the younger kids?
Probably. If there is one thing those Japanese are known for, not including all the weird stuff, is that they have work lives that can regularly work them to death. The dad's hours could very well be insane, and he would have to get a different job if he had to be back in time to make his children supper.