Is it permissible to sell a house for which a portion of the price has been paid before the full amount is settled? And is it permissible to calculate a percentage of the profit for a partner whose money was not actually used in the purchase due to the quick sale?

It is permissible to sell a property that a person owns, even if there is still an outstanding deferred payment from its original price, as the decisive factor is the completion of the first sale and the transfer of ownership. However, if the buyer has not yet taken possession of the property, it is not permissible for him to sell it, based on the Prophet's (peace be upon him) saying: "Do not sell what you do not possess."

As for the question about partnership in real estate trading, it is unclear, as the rulings on partnerships vary depending on their conditions. It could be a capital partnership or a credit partnership, and each has its own rulings.