Yes! i;m getting the same answer as yours for ii and iii.
To Where (Pave/ peak gate power) = Duty circle
Duty circle = Ton / (Ton + toff)
Ton given, Duty circle is apply in order to find Frequency by using F = 1/Period.
However i;m still dun get how could u got the answer for i).
Added after 44 minutes:
Here is my solution for finding the gate resistance.
Pg = VgxIg <-------1
Vg = 1 + 10Ig <------2
since the Pg is given as 5 W, (5/Ig) = Vg <-----3
substitude equation "3" inside equation "2"
u will be able to getting the equation 5 = Ig + 10 (Ig^2)
Ig = 0.65 A and -0.75A (neglect)
Vg = 1 + (10x Ig)
Vg= 7.5V
Rg = (Vamplitude - Vg) / Ig
V amplitude = 15V
Rg = 11.53 ohm