Finding the transfer function of a discrete signal described by two equations
HINT:

(because it's a homework problem)


Apply the $\mathcal{Z}$-transform to both equations. Use the first equation to express $Q(z)$ in terms of $X(z)$, and plug that into the second equation to obtain $Y(z)$ in terms of $X(z)$. From this you can easily get the transfer function $H(z)$.
Compute the poles and zeros of $H(z)$ and determine the constant $k$ such that the system is stable and/or minimum-phase. You should know what stability and minimum-phase mean in terms of poles and zeros (if not, it should be easy to find that online or in a textbook).