Those pieces you found might be counter weights that provided engine balance. If the crank shaft is light opposite the piston, metal weight might be welded on. If the crank shaft is heavy opposite the piston, holes might be drilled in the shaft to remove metal. If you can determine that those pieces were welded on, perhaps you can re-attach them onto the original positions.
If the crank shaft is bent, it is more than likely bent outside the motor.
When the engine is back together but before you install it on the mower clamp something stationary to it. A tool or piece of metal or wood that is near but not touching the shaft where the shaft extends from the motor, but as far away from the motor housing as possible, can tell you if it is bent. When the engine is turned the distance between the shaft and the clamped on piece should remain exactly the same. If there is any change in the distance you know the shaft is bent. A bent shaft can be straightened.
This is video is not showing a motor with a pully, but the principle is the same.
I've straightened a few shafts using this redneck method ;-)