What altitude turboprop engine can fly?

That depends on a few things. How big is the plane, how many engines does it have, how many blades on each propeller, etc. More blades will let the aircraft keep moving forward and maintain lift at higher altitudes where the pressure is low, but if speed isn't the problem, then the question is if the engine can get enough oxygen to keep the engine running. If the pressure is too low, then the engine will stall and shut down. Restarting the engine again after having fallen to a lower altitude ought to work. As for the average ceiling, I'd say no higher than 40,000 feet if you can get that high, probably 30,000 feet would be the ordinary limit.