Have you written the landlord and confronted them on this issue? If not, then I would suggest you do, and include the fact that you have emails from prospective tenants writing you that your unit is not available.
Also, when you terminate your lease and turn in the keys, you are no longer a rightful tenant. Therefore, the landlord is not obliged nor bound by law to surrender the keys to you. You are, however, bound by the agreement to pay the lease amount until they rent the unit AND the landlord must rent the unit as soon a possible (mitigate their damages).

