Is the contract considered renewed based on the renewal letter signed by the deceased owner, and what is the legitimate ruling when some heirs refuse to renew, even though they do not possess an absolute majority in the leased property?

It appears from the question that what transpired between the owner and his son was a power of attorney from the owner to his son to renew the contract. This power of attorney becomes void upon the owner's death, as an agency agreement is nullified by the death of the principal, by consensus. The right to the property has now transferred to the heirs, and they are not bound by their deceased's power of attorney. Furthermore, some of the heirs do not have the right to lease the property without the consent of the others, because each heir has an undivided share in it. The final arbiter in this dispute is the Sharia (definition) judiciary.