I’ve got a problem with understanding propeller windmilling. What I know is that when rpm are low and tas is high the blade aoa goes „over” the blade and is some kind of negative now, producing thrust in opposite direction than usual. But I don’t understand what really happens there. Is prop rotating in opposite direction or sth? I also read somewhere in the atpl book that when prop is windmilling the prop is driving the engine. How is that possible? Can somebody clarify that to me?
You can think of the propeller as a screw. Take a screw, a screwdriver, and starts screwing. The threads of the screw drive the screw into the block of wood.
The propeller works in a same way: the engine drives the propeller that "screws" through the air.
It also works the other way around. Well kind of, with the screw, because of the high friction between the block of wood and the threads of the screw, but forget about the friction for a while, if you can.
If you stop twisting the handle of the screwdriver, and instead push the block of wood against the screw + screwdriver combo, what should happen? The screw should rotate just as if you were screwing it with the screwdriver, as the threads are still sinking deeper into the block of wood. The screwdriver would of course rotate with it.
Again, it's the same with propellers (and engines). If you have speed, and you shut down the engine, the airflow will push against the propeller just as the (magically frictionless) wood against the screw. The propeller will keep rotating in the same direction, and as it does so, it keeps the engine turning also.
Now, in the case of you no longer twisting the screwdriver handle or the engine driving the propeller, there is no longer a force driving the screw or the propeller through the medium they are engulfed in. Instead, the medium (wood or air) is imposing a force on the screw & the screwdriver, or the propeller & engine to keep them turning.
If you do a google image search with words "propeller tip contrail" you'll find pictures displaying nicely how the propellers are actually screwing their path through the air.
When windmilling, the propeller rotates in the same direction as when propelling the aircraft.
Picture above was also included in this answer, and shows the local Angle of Attack at the blade profile: a vectorial summation of rotational speed of the prop, and airspeed. As long as the AoA is positive, spinning the propeller by applying engine torque will create thrust. This is essential: torque rotates propellers.
Now stop applying engine torque to the propeller, and its rotational speed will decrease. Airspeed decreases much slower, so the AoA of the prop blade will decrease. At negative AoA, the incoming air flow will apply the necessary torque for turning the propeller, as depicted above right hand side. The windmilling propeller turns the same way.