A simple, experimental motor such as this is not capable of making much power. We can increase the turning force (or torque) that the motor can create in three ways: either we can have a more powerful permanent magnet, or we can increase the electric current flowing through the wire, or we can make the coil so it has many "turns" (loops) of very thin wire instead of one "turn" of thick wire. In practice, a motor also has the permanent magnet curved in a circular shape so it almost touches the coil of wire that rotates inside it. The closer together the magnet and the coil, the greater the force the motor can produce.
Think of the atoms of magnetic material as an unruly herd of cattle. Running electric current through the material will polarize these atoms, creating the magnetic field. But as I mentioned, this is an unruly herd, so it takes time for the current to bring all those atoms into formation.
The shield strongly attenuates the electric field noise. Core to shield capacitance is added to the stray capacitance, increasing ground currents in the loop. These currents generate a magnetic field. It is important to minimize the area of this loop as far as possible by routing the cable close to grounded metalwork.
If you place the wire near a permanent magnet, this temporary magnetic field interacts with the permanent magnet field. You will know that two magnets placed near one another either attract or repel. In the same way, the temporary magnetism around the wire attracts or repels the permanent magnetism from the magnet, and that is what causes the wire to jump.