The strength of the magnet has to do with how well the magnetic domains are aligned. if they are very well aligned, you have a stronger magnet. Dropping the magnet literally breaks up the domains, and causes the atoms to be more randomly oriented. This decreases the strength of the magnet. The magnetic field lines are actually curved in a circle about the wire. A charge moving parallel to the magnetic field lines, experiences minimum deflection , but a charge moving perpendicular to the field lines experiences maximum deflection.
Induction occurs when a magnetic field changes with time.
Both are based on the fundamental premise that the current, magnetic field, and resulting force are all mutually perpendicular. This can be used to create a torque on a loop of wire, causing it to twist. A motor requires an input current, which causes the coil to rotate. Because the attraction is due to the magnet pulling the unmagnetized domains of the iron into alignment. Whether the magnet is brought close to the N or S pole of the magnet does not matter.