According to my corrected magnetic force law, parallel currents attract each other and anti-parallel currents repel each other, see Theory about parallel action experiment. So, for the rectangular coil near the solenoid in Figure 1, the upper current is parallel to that in the front side of the solenoid and the lower current is anti-parallel. So, there would be a torque created on the coil and the coil should rotate.

However, the magnetic field outside a solenoid is zero and cannot act any force on a current. Moreover, there cannot be force parallel to current for classical theory.

So, If I do this experiment, will the coil rotate or not?

Please read the article at
Q: Parallel action with a solenoid
http://pengkuanem.blogspot.com/2015/05/q-parallel-action-with-solenoid.html
or
https://www.academia.edu/12426677/Q_Parallel_action_with_a_solenoid