Am I, as my father's heir, entitled to a percentage of the store's management, especially since I perform most of the administrative and sales tasks? And what is the ruling on selling goods at a deferred price, with its price to be determined after a week, or selling them in installments and then the buyer requests to reduce the installment and extend the period?

It is permissible for people to share their capital while some of them provide the labor. In this case, it is permissible for your father and uncle to take 50% of the profit in exchange for management. The remainder is then distributed based on capital. Note that this management right is not inheritable and becomes void upon the death of either partner. The partnership can be dissolved at the desire of any party. The manager can demand a change in the contract, take over management, or withdraw from the company. It is not permissible to sell goods at a deferred price and determine their cost after the buyer has received them. Increasing the price in installments in exchange for extending the period is forbidden usury (riba). However, reducing payments without increasing the price is permissible. It is not permissible to engage in forbidden transactions or to assist in them, especially if the partner is directly involved in the forbidden act, because he acts on behalf of the partners, and authorizing a forbidden act is not permissible.