What is the Sharia ruling on the described sale process, and what is the ruling on its parties (the intermediary, the buyer, the seller, the bank), and what is the ruling on the intermediary's fee? And if there is anything unlawful in it or in its clauses, what is the lawful way to conduct it?

The aforementioned sale is Murabaha for one who promises to purchase, and it is permissible under the following conditions:

1. The bank must first own the property and bear responsibility for it.

2. The property must be sold to the buyer in installments at a fixed price that does not change.

3. The promise to buy or sell must not be binding, because if it were binding, it would become a sales contract contingent on a future condition, which is invalid.

Based on this, the owner's promise to sell to the bank cannot be considered binding.

As for your work as a mediator between the parties (owner, bank, buyer), it is brokerage, and taking a percentage as a fee for it is permissible.