What is the ruling on the amount paid to the employee to terminate a delayed lease, and what is the ruling on the money earned from subsequently leasing the shop, and can this money be used for Umrah?

If the shop is owned by your father and the state imposed restrictions preventing the ownership of more than one shop, then what you paid to get rid of that is considered permissible circumvention, and the sin is on the taker, not on you. This is because forbidden bribery is for nullifying a right or validating falsehood. However, for repelling injustice or obtaining a right, it is permissible.

If the shop is owned by the state and your father leased it from them, then the contract is valid, and previous indebtedness does not affect its validity. Your father is obligated to pay the rent for the period he benefited from the shop, as well as the period he himself closed it. However, if the state closed it, he is not obligated to pay the rent for that period.

Whatever amount was due from your father must be paid, and it is not permissible to pay a bribe to waive it. However, for what was not due, such as usurious interest and unlawful taxes, it is permissible to circumvent to waive it, even by paying a bribe, and the sin is on the taker.