All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
Rent-to-own contract according to the form that is known to economists is impermissible as it includes many violations of Sharee‘ah (Islamic law) rules such as uncertainty, as the lessee may be unable to pay the last installment and in this case, he would lose all that he had paid. This is because the real estate will be returned to the property owner and this makes him take both the lease and the real estate. Moreover, in this contract, the installments that the lessee pays are usually more than the real lease of that real estate.
The Islamic Fiqh Academy offered two Sharee‘ah–approved alternatives: The first one is selling on installments while obtaining sufficient guarantees. The second one is to conclude a lease contract whereby the owner gives the lessee the option to extend the lease term, end the lease contract and return the real estate to its owner or purchase the estate after the lease period and full payment of the due rent at the prevailing market price.
As for the kind of purchase that you mentioned which entails paying a fine in case of delayed payment, it is prohibited as this is pure Riba (usury).
As for the third point that you mentioned, it would be alright if the company, institution or bank bought the real estate from the owner then leased it or sold it on installments to a third party provided that this sale does not include any of the prohibited conditions as what you mentioned above.
Allaah Knows best.