My mechanics are a bit rusty, but i think this is right...
For part c, u kno that T1>0, but T2 may not necessarily be 0. Since both tensions have to be positive, set T2>0.
T2=mrw^2-mgsin(theta)>0
rw^2>gtan(theta)
Since r=4asin(theta),
4aw^2sin(theta)>gtan(theta)
4aw^2>gsec(theta)=5g/4
Therefore...