Which of the following problems are decidable? 1) Does a given program ever produce an output? 2) If $L$ is a context-free language, then, is $\overline{L}$ also context-free? 3) If $L$ is a regular language, then, is $\overline{L}$ also regular? 4) If $L$ is a recursive language, then, is $\overline{L}$ also recursive?

Let us analyze the decidability of each statement:

1. Does a given program ever produce an output? This is equivalent to asking whether a Turing machine enters an output-producing state (a non-trivial semantic property of the language), which is undecidable by Rice's Theorem / the Halting Problem.

2. If $L$ is a CFL, is $\overline{L}$ context-free? Determining whether the complement of a context-free language is also context-free is undecidable (and context-free languages are not closed under complementation).

3. If $L$ is a regular language, then is $\overline{L}$ also regular? Regular languages are closed under complementation. Thus, the complement of any regular language is guaranteed to be regular, making this a trivially decidable property (always true).

4. If $L$ is a recursive language, then is $\overline{L}$ also recursive? Recursive languages (decidable languages) are closed under complementation. Thus, the complement of any recursive language is always recursive, which is also trivially decidable (always true).

Hence, statements 3 and 4 are decidable (Option D).