Current passing through zener diode at base of NPN
Are you calculating the base current or Zener current?  The base voltage will be 10V, so the emitter voltage would be 9.3V.  The emitter current would be 9.3/10 = 0.93A.  Base current would be 9.3mA.  The voltage across the base resistor is 10V, so the current is 20mA.  The Zener current is Ir - Ib = 20 - 9.3 = 10.7mA