Is it permissible to sell an apartment subsidized by the state, with its installments accumulated, if the waiver agreement requires the approval of the owning authority and considers what has been paid as rent, and is this sale considered a "khalaw" (premium for vacating property)?

If you bought an apartment in installments, and the contract stipulated that upon inability to pay, your ownership would be forfeited and the amount paid would be considered rent, then this is a void condition due to the presence of gharar (excessive uncertainty) and the combination of a sale contract and a lease contract. However, this condition does not invalidate the sale contract, so you are permitted to sell the apartment. But if it is mortgaged, you must first repay the debt or obtain permission to sell from the owning entity.

If the apartment was leased to you with the agreement that you would own it at the end of the lease term, then this is a void lease contract. You are not permitted to sell it or assign its lease for compensation. The contract must be rescinded, and you must reclaim any amount paid in excess of the fair market rent.