Comments:

1. In Q1, the system is stable. A system is stable if the ROC contains the unit circle. If the system is causal, that means all the poles have to inside the unit circle (not on the unit circle either) for the system to be stable. If the system is anti-causal, then all the poles have to outside the unit circle for stability.

2. In Q1, the phase of $ H(\omega) $ is an odd function.

3. In Q2 and Q3, there are eight different zeros: solve $ z^8=1 $. The pole at z=1 subsequently cancels with the zero at z=1.