On the stability and causality of a discrete system
To your first question, a linear system is causal if we have initial conditions of rest that is zero. This is a sufficient and necceassy condition. This property doesn't  require time invariance

Stability is a consequence of absolute summability of system response. It doesn't depend on the initial condition (of course have to be finite to make any sense).

To your second question the transfer function has a pole at z=3 and it is given that the system is stable. That means the ROC has to include the unit circle. That means that the ROC is to the left of the pole at z = 3, since ROC is towards the left of outermost pole hence system is not causal