Is it permissible to demand a 10% increase on the refunded money after canceling a commercial shop rental agreement that included merchandise, knowing that the amount paid was less than half the value of the merchandise, and the agreement was to pay the remainder monthly from the shop's profit?

A sale is a binding contract for both parties. Neither party has the right to unilaterally revoke it unless the other party agrees, or unless there was an option clause. Revocation (Iqalah) is a cancellation of the contract. According to this view, revocation is not permissible with an increase in price. Therefore, it is not permissible for you to take an increase over the price at which you bought those goods. However, if the contract is revoked and a new sales contract is established, and you sell those goods back to the seller with a profit, then there is no problem in that case. If you bought it for a deferred price, or half of it was deferred, then it is not permissible to sell it for a lower cash price. Rather, it must be sold for the same original price or more, in order to avoid falling into the prohibited 'inah transaction.