Question about fly-back diode
1) An inductor's current remains flowing in the same direction when open circuited and the only way this can be achieved is by reversing its polaity so you can't have both.

2) When the voltage is zero the current flow is at a maximum but this energy feeds back into the voltage source hence no spike - the spike only happens with non zero-ohm voltage sources with discontinuous signals.

3) Generally there are diodes but they are probably on the circuit that drives the motor and might easily be inside some chips.

4) No an LED won't withstand much in the way of reverse voltage (maybe 5V) so any motor supply greater than 5V might destroy it but ostensibly it will work.