I believe that "A given B" means "If B, then A". So, "x parties with carmen given that x questions himself" means "if x questions himself, then x parties with carmen", while the formula has the converse implication. But you are right that b is a counterexample.

You are free to come up with an interpretation for abstract symbols to get a better intuitive idea of what the formulas say. I do this myself sometimes when formulas are complicated. For this problem, it is probably easier for me to think "as is". For example, Q is "almost" reflexive; the only exception is b. If Q were reflexive, then ∀x(P(x,c) ⇒ Q(x,x)) would be true just because the conclusion is true. So, the only x to check is b. And indeed, x = b makes the premise true, so the implication is false. For (c), we can take x = b again; then the premise of the implication is false and the implication is therefore true.