Is it permissible, in Sharia, to agree upon a fixed daily payment for a taxi driver, regardless of profit or loss, given that the authorities are fighting against such an agreement?

The scenario mentioned in the question is impermissible due to the failure to fulfill the condition of knowing the rental fee, which eliminates ambiguity that could lead to dispute, and might result in injustice to the driver. The transaction can be corrected by the driver renting the car for a known duration and at a known fee. In this case, he would be a renter who owns the usufruct of the car and has the right to use it for his private purposes, as opposed to being an employee in the first scenario. A Muslim should respect the laws of the country in which he resides, as long as they do not conflict with Islamic law.