Decidable language: set of context-free langauges containing 1 string
Hint: The point of this exercise is that it is decidable whether a context-free grammar generates the empty language. Using this as a black box, you can proceed as follows. On input $G$:


Check if $L(G)$ is empty, and if so, reject.
Find a word $w \in L(G)$.
Check whether $L(G) \cap (\Sigma^* \setminus w)$ is empty.


I'll let you figure out how to implement the latter two steps; step 2 uses the fact that it is decidable whether a grammar $G$ generates a given word $x$, and step 3 uses the fact that the intersection of a context-free language and a regular language is context-free (constructively).

The same idea can be used to calculate $L(G)$ given that we know that $L(G)$ is finite.