Q1. False: the term "search problem" is not related to vertex/path finding in a graph. The mention of "Dijkstra's", a polynomial-time algorithm, was a hint that it would not be appropriate to apply it to NP-complete problems that are conjectured to take more than polynomial time to solve. Q2. False: the search formulation of CLIQUE should also have a target $k$ such that the goal is to find a clique of size $k$, specifically. Another way to think about it is: any graph with at least 1 vertex trivially has a clique of size 1 (i.e. any vertex), so this formulation wouldn't be an interesting problem.