Are there more languages than functions?
It depends on the signature of the function.  In computability theory we typically deal with functions with the signature $f:\{0,1\}^* \to \{0,1\}$.  There is a one-to-one correspondence between functions $f:\{0,1\}^* \to \{0,1\}$ and languages $L \subseteq \{0,1\}^*$: in particular, the function $f$ corresponds to the language $L=\{x : f(x)=1\}$, and the language $L$ corresponds to the function $f(x) = 1$ if $x \in L$, $f(x) = 0$ if $x \notin L$.