Is a single symbol, not in a set, a language?
By the standard definitions, a language is always a set of (finite-length) words. This means that "$a$" is not a language, but either a symbol or a word. 

If $R$ denotes all the regular languages (or alternatively, all the recursive languages), then indeed $a \notin R$. On the other hand, $\{a\}$ is a language, which is also regular (and recursive).

To complete the standard definitions:


an alphabet is a finite set of symbols
a word is a finite-length string of symbols
a language is a set of words (and can be finite or infinite)


of course, there are many possible extensions to the above definitions, such as infinite-alphabet, infinite-length words, etc.