Is it permissible for my maternal uncle to rent out a shop, which is legally disputed, for an amount exceeding what he pays to its original owner, and to pay the taxes from this money?

The majority of scholars hold that a lease (ijarah) is not terminated by the death of either contracting party (lessor or lessee). Rather, the contract remains valid, and the right of usufruct (intifa') transfers to the heirs of the lessee. Similarly, a lease contract is not terminated by the sale of the leased property. In this case, the purchaser acquires the property with its usufruct already encumbered until the end of the lease term, and the right of usufruct remains with the lessee. The lessee is permitted to sublease the property to another under specific conditions. As for a perpetual lease (ijarah mu'abbadah) that grants the lessee the right of permanent occupancy, it is invalid according to Islamic law, and the lessee must return the property to its owner.