If deceased father's debt is not paid off and the eldest son is buying stuff for his own house, is it permissible? And buying new clothes for him and his family?

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If you are asking about using the heritage/inheritance, before settling father's debt, then it is not allowed.
But if he is buying from his own money, then, it is Okey.
On the other hand, settling father's debt -if he did not left any heritage- is not the eldest son sole responsibility.