Is the aforementioned transaction with Al Rajhi Bank permissible by Sharia, which involves buying palm oil from the stock market, then selling it to me and staggering the payments, along with my authorization to the bank to sell it? If it is not permissible, do I have to return the remaining amount to the bank, or is sincere repentance sufficient while using the money for building a house?

The transaction mentioned with the bank is Murabaha for the one who orders the purchase. If the purpose of buying the commodity is to sell it to obtain cash, then this is a permissible Tawarruq, subject to its conditions.

However, the palm oil exchange is not permissible, due to the lack of actual ownership and utilization of the oil, as well as selling food before taking possession of it, as it remains in the suppliers' warehouses. This contradicts the prohibition of the Prophet (peace be upon him) against selling food before taking possession of it, and the consensus of scholars on this matter.

Nevertheless, if the bank has a trustworthy Sharia (definition) board that has issued a fatwa (definition) permitting the Tawarruq transactions conducted by the bank, then there is no harm for you in following them, for the madhhab (definition) of a layperson is the madhhab of the scholar who issues him a fatwa.