I can reproduce a significant FPS drop, but only with my Carenado planes. I start with very good FPS cold and dark, but performance drops by around 10-20 FPS (!) once I start the engine. If I turn the engine off again, FPS is recovering. This does not happen with the default X-Plane C172.
Machine is i7-2700K @4.9GHz, GTX 770 4GB, 16 GB Ram
Yes, that's usually the case. Windows changes the core for execution of a thread many times per second. That's the reason why you see the distribution of the load to several cores. I agree that this is misleading in the task manager visualization, but in most cases, there is one very demanding X-Plane thread involved that's the bottleneck.
You have twelve cores. If the CPU load is at 12, this indicates that one thread is maxing your CPU.
So, it seems that the most demanding thread in X-Plane is limiting your performance on your CPU.