Is it permissible for someone who collects the salaries of his siblings and manages their affairs to buy something personal for himself from this commingled money, knowing that his siblings' basic expenses may be greater than his own expenses?

The agreed-upon rule for managing shared funds is what has been agreed upon by the partners or what is customary. If the money is allocated for consumption and household expenses, there is no blame on whoever takes from it for this purpose. The reference in this regard is custom and the رضا (consent) of all. However, if it is for other purposes, it is not permissible to dispose of it except in accordance with what it was designated for. And whoever takes anything from it without the knowledge of their partners is an aggressor and is liable for what they took until they return it, based on the saying of the Prophet, peace and blessings be upon him: "On the hand is what it took until it returns it," and based on the saying of Allah the Almighty in the Qudsi Hadith: "I am the third of the two partners as long as one of them does not betray his companion; if he betrays him, I depart from between them."