Is the questioner considered disobedient to his mother if he does not help her with household chores, especially since he is busy with studying and his mother refuses his help to her?

The son is not disobedient to his mother for not financially assisting her in the mentioned circumstance, and his striving for success, which pleases her, is a form of dutifulness to her. Bringing joy to the mother is among the greatest forms of dutifulness. He should help her during his vacations and advise his siblings to be dutiful to their parents or to provide a servant for her. He should also frequently supplicate for his mother and siblings.