Q1: Yes, {r} is the sink state, in the sense it is that state that is added as target state by the subset construction for the missing transitions. But also {q} is a sink state.
Q2: We do not need state {r,q} in the sense that the subset construction does not generate that state. However, as we encode the states by two state variables, we get four states and have to deal with the fourth state.
Q3: The transition relation can be encoded in different ways. Since it is deterministic, one can also write it as a conjunction of equations
(r′ ↔ r ∨ ¬r∧¬q∧¬a∧¬b) ∧ (q′ ↔ q ∨ ¬r∧¬q∧b)
(See also the updated example solutions)
