First, recall the theorem which states that the congruence , where is a polynomial of degree with integral coefficients, has at most solutions (Niven, An Introduction to the Theory of Numbers, ch. 2, sec. 7). In particular, these quadratic congruences will simply have plus/minus a natural number less than its respective prime.
With that in mind, we needn't perform any detailed calculations. The numbers are small enough that trial-and-error works just fine.
So, in other words, all your answers are correct except that in part (c).