Is the eldest brother, who undertook the sale of his deceased father's properties and the collection of the inheritance, entitled to deduct travel and accommodation expenses and any resulting material damages from the inheritance money, and does this require the approval of the heirs?

Whatever is spent appropriately on the work entrusted to you by the heirs, it is permissible to recover it from the inheritance funds. As for payment for the effort expended or compensation for damages, it is not permissible to take it from the heirs' money without their knowledge and consent, unless it is customary for you to receive payment for such work and you were not performing it as a volunteer. In that case, you are only entitled to the customary wage, unless all adult heirs agree to give you more.