What am I permitted to take from the wealth of my deceased relative, knowing that I am covering the expenses of the inheritance inventory and performing tasks myself that require significant funds, and am I obligated to repay his debts and bank claims with interest, which he refused to pay?

If you spent money on inventorying the estate, you may take a similar amount, unless you acted as a volunteer. As for your work wages, if you are an executor and poor, you may take the lesser of the customary wage and what suffices you, as is common practice. If you are wealthy, you are not entitled to take anything. If you are not an executor, and you volunteered, then you receive nothing. If you worked with the intention of being paid, then you are entitled to a customary wage. Regarding the dispute between your relative and the banks, we advise you to refer to the Sharia court.