Questions about regular languages and their sublanguages I am interested in the following questions and would be grateful if anyone could give me hints or point me to articles:

1) Given a regular language $L$, what are its regular sublanguages $L'\subseteq L$, i.e. how to enumerate all regular $L' \subseteq L$ for a given regular language $L$.

2) Could every regular sublanguage $L'$ of a regular language $L$ be written as $L' = L''\cap L$ with $L''$ regular

3) Given a arbitrary language, is it decidable if it is regular (of course one could compute it's syntactic monoid, but this computation could take on forever if the language is not regular)
3) It is undecidable to know whether a given context-free grammar generates a regular language. So even for context-free languages, you are in trouble.