Is the money saved and the piece of gold left by the mother considered an inheritance to be divided among the heirs, or does their ownership transfer to the questioner who was spending on her?

What you gifted to your mother during her lifetime, you will be rewarded for. What remains after her death belongs to all her heirs, even what you gifted to her, because by gifting it, it ceased to be your property and became hers. After her death, it became the property of her heirs, and you are one of them, so it should be distributed among you according to Islamic law. As for the apartment, if it was owned by her mother, it belongs to the heirs. If it was rented and the rental contract has not expired, the benefit of the rent belongs to the heirs because the rental contract is not annulled by the death of the landlord or the tenant. The rent remains a debt against the estate. If there is no estate, the heir is not compelled to pay it, and the rental agreement is annulled. If the brother volunteers to pay the rent and the heirs waive their right to live in it for him, then the benefit of living there becomes his.