2. its the cross product of charge's velocity and the mf. If you point your fingers towards the direction of the velocity then point your palm in the direction of the mf (either up or down), then your thumb will be pointing to the direction of the force acted upon by the mf on the charge.
so, its always perpendicular to the mf, and perpendicular to charge's velocity if it is also perpendicular to the mf.
5. break the velocity vector into a parallel component and a perpendicular component. disregard the parallel component since it doesn' cause any force from the mf. Then use the perpendicular component in the equation.
These are very good inquiries. First of all, the magnetic field vector field was initially defined as the direction in which magnetic dipoles align. It is important to understand that the alignment of magnetic dipoles in B-fields due to magnets, such as iron, is caused by the same force that causes deflection of moving charges.
Take a square of wire that lies in the x-y plane with a constant current (movement of charge) flowing through it (in say the positive phi direction). Then let us apply a external uniform B-field, in say, the positive y-direction. Now, the ring of current is going to produce its own B-field independent of the externally applied B-field due to Biot-Savart's law and the magnetic dipole moment due to this B-field is in the positive z-direction, dictated by the current direction. In addition, the ring of current will begin to rotate in the presence of the external B-field, due to the Lorentz force. It is clear that the Lorentz force will want to align the current ring's magnetic dipole with the external B-field.
Now, the alignment of iron shavings with a B-field is caused by the same action. In all materials, the electrons around the atoms (bound or unbound) are moving which produce magnetic dipoles. In the absense of a B-field, the magnetic dipoles are pointing in random directions. However, in some materials (magnetic materials), in the presense of a B-field the magnetic dipoles align themselves with the B-field. This is caused by the same physical laws that cause a current ring's dipole to align with a magnetic field. Some materials do not align their at all dipoles with the magnetic field. These materials are non-magnetic. Other materials allow their magnetic dipoles to align with the B-field but when the B-field is turned off the dipoles point in random directions once again. Other materials after the dipoles are aligned by a B-field and then the field is turned off some of their dipoles stay in the direction induced by the B-field, but the rest resume their random orientations (these are called paramagnetic or diamagnetic substances). Finally, other materials after the dipoles are aligned by a B-field and then the field is turned off most of the dipoles retain their aligned orientations (these are called ferromagnetic substances).
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