decidability about intersection of regular language and context free language
It is known that the intersection of a regular language and a context free one is context free. Besides, you can always take your regular language to be $\Sigma^*$, so any context free language can be the result.
Then the question is if a given context free language is empty, which is easy to answer.
To ask if the complement of a context free language is empty is to ask if it is $\Sigma^*$, which is undecidable.