Why would a repairman install a 1/3 HP fan motor into a 1/5 HP unit?
Most likely because he had it on hand. Possibly leftover from an unrelated ordering error, so he was chuffed to use it in a chargeable account. If all the other characteristics were similar, there's nothing wrong using a somewhat oversized motor. It's a big IF though. For instance, the larger motor may have overloaded the starter circuit, frying the capacitor. No accusations here, this is pure conjecture.

No matter what, it should have lasted more than 2 months. It was either defective, or there's something inherently wrong with how it's installed that greatly shortens motor life. Backwards is a rather comical rookie mistake, easily caught if someone bothers to check their own work before leaving.

A pretty flippant comment that some units only last 4 years. He's somewhat correct in that a rare few units fail prematurely due to some defect in manufacture. But expected lifespan is quite a bit longer.

We might write this off as a fluke, but if you have another motor failure, an investigation for a contributory factor would be warranted.