Rectifiers operation when there is a sudden voltage drop
What happens now with the current /voltage on the inductive load? Then
  again it can't simply just drop to zero, in the case of the current.
  But where to does the inductive load discharges?


It discharges into a voltage source, the inductive load becomes a generator for that amount of time. Thyristor conducts the current as before (until the current drops to zero), there is no current break only the voltage is now reversed, therefore the power becomes negative - it is flowing back to the source.


  In a full-bridge rectifier supplying an inductive load, if there is a
  sudden drop on the AC voltage at the input of the rectifier, the
  firing angle will immediately drop to zero degrees


Usually is the control circuit which defines the firing angle and not the thyristor by itself.


  Now if there is a breakdown and the gate current/voltage of the
  thyristors suddenly drops to zero, they will cut off, right?


No, because thyristors are ignited with a pulse, and they stop conducting by themselves (they are latching) when the current through drops to a minimum holding current.