Is it permissible, Islamically, to purchase a property under construction with the intention of selling it for profit, by directly transferring the contract to the new buyer? What amendments are necessary to make it permissible? Is it permissible to take a commission for mediation in this process? What must be done to make it permissible?

It is permissible to purchase properties under construction, either in cash or in installments, as this falls under the category of an istisna' (manufacturing/construction) contract. However, it is not permissible to sell the property until after it has been received, due to the Prophet's (peace be upon him) prohibition of selling what is not in the seller's possession and earning profit from what has not been guaranteed. To rectify this transaction, the contract between you and the seller is annulled. Then, the seller enters into a new contract with the buyer, and you act as an intermediary, receiving the down payment and a profit for your mediation. This mediation is permissible and is known as brokerage (samsara), and it is permissible to receive a fee for it.