Is it considered gambling to agree with a mechanic on a fee for repairing a car part without actually repairing it, or to drive a broken-down car with the risk of it either being repaired or breaking down further?

The transaction mentioned in the question is permissible and does not fall under gambling. The outcome attributed to the mentioned transaction, "either it gets fixed and he profits, or it breaks down and he loses," is incorrect. Rather, either the mechanic fixes the defect, in which case he deserves the wage, or he does not fix it, in which case he does not deserve it.