Questions about example exam

in question 1,
not all inputs are satisfiable (for example A=B=7), who am I supposed to implement the circuit considering this?

in question 2,
is initialize a given or am I supposed to implement it as well? also, there is no desirable Y(t) if OP(t) == 1. does that mean that we shouldn’t care about it or decide a rule for it our selves?

in question 3,
is g(x,n) given as a blackbox? in general, when can we use a given circuit as a blackbox if we are not asked to implement it ourselves?