Can someone please help me with these questions on DC Chopper Circuits?
I will try to answer question 1. In "continuous operation mode" (current in coil never falls to zero), the output voltage of a buck converter is Vout=D*Vin, where D=50% is the duty cycle and Vin=100V. So you know that Vout=50V and thus Iout=Vout/R=5A. 

Next, remember the inductor equation V=L* dI/dt. V is Vin-Vout=50V. dt is the time the switch is on or off. dI is 0.2*Iout.

This equation can be formed to L=V*dt/dI, where V=50V, dt=1/(2*f)=5us and dI=0.2*Iout=1A. 

So Lmin=250uH