Is the questioner sinful if she does not help her younger brother with his homework, knowing that he makes no effort, and her mother gets angry if she doesn't? And is she obligated to clean and tidy the house by herself instead of her siblings who participate in messing it up?

Obeying parents is obligatory, unless it involves disobeying Allah or causing harm to the child. Providing ready-made answers to your brother for his homework assignments is not permissible because it constitutes cheating, as the Prophet (peace be upon him) said: "Whoever cheats us is not of us." Therefore, your mother should be advised regarding this religiously forbidden act and misguided parenting. Furthermore, the unruly behavior of your siblings is unacceptable; they should help tidy the house instead of messing it up. They should be advised kindly, and your mother must fulfill her role in guiding and caring for them.