Is it permissible to take a fee (fuel allowance) from a colleague at work when giving him a ride in the car designated for work?

An employee is not permitted to dispose of his employer's assets except with explicit or customary permission. The company does not authorize the employee to use the car allocated for his transportation as "capital from which to earn a living," because it grants him personal usufruct, not ownership of the usufruct that includes renting or lending to others. Accordingly, it is not permissible to use the company car in the manner mentioned by the questioner.