Is purchasing a house through financial leasing institutions, where the institution buys the house and it remains under its ownership, and installments are paid to it until ownership is transferred to the buyer, considered a legitimate alternative to usurious loans, and what are the necessary conditions to ensure the permissibility of this transaction?

If the company will buy the house and lease it to you through a lease-to-own agreement (ijarah (definition) muntahiyah bi al-tamleek), then there is no harm in that, provided the contract adheres to the Sharia (definition)-compliant stipulations. Among the most important of these is that the lease should not be a mere cover for a sale. Rather, the two contracts (lease and sale) must be separate, and the sale contract should be concluded after the termination of the lease contract, or based on an existing promise to transfer ownership.