What is my financial duty toward my siblings, and what are their lawful rights, especially after they demanded that I pay back the amount they spent on me during my studies, which my brother sponsored, knowing that my father did not spend on us and my mother worked to take care of us?

If your brother spent money on you with the intention of being repaid, you must repay him if you had the money at the time he spent it. However, if he spent on you as a donation, he is not permitted to demand the money back, based on the hadith: "The one who takes back his gift is like one who eats his vomit." It is recommended for you to reward him and treat him kindly, based on the hadith: "Whoever does you a favor, then reciprocate it," and "Exchange gifts, and you will love one another." It is also good for you to spend on those in need, and you must honor your father regardless of how he treats you.