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If everything is symmetrical, and it still goes into a flat spin power-off, you probably need to move the CoM forward, and/or increase the size of the rudder. As for what happens power-on, I've seen few single-propeller machines on Besiege that have any real directional stability at all - balencing out the torque in a controlled manner is difficult.
Even an unpowered wheel will deliver some torque - it isn't friction-free. And I'm not sure that Besiege's physics works quite like the real world when it comes to torque effects - the way people use wheels as 'reaction control' suggests to me that it doesn't.
I would not recommended for you to use as an wing as the body. Use brace + Ballast (0.2 mass)
Also, check the elevator or the rudder if they are straight. If not, mod it.
Sometime in Besiege Physic, which in air, when the wheel turn on, it pushes the air like the wheel pushing the water going in circle.