Question Describe the language of $S\to0S0\,\,|\,\,1S0\,\,|\,\,\varepsilon$.
$L=\{\Sigma^{n}0^{n}\,\,|\,\,n\geq0\},$ but I'm not sure that's an accurate answer.
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Your description is accurate, as far as that goes, with the proviso that should explicitly state that $\Sigma=\{0, 1\}$. The question is whether that's the kind of description you're being asked to provide.
For example, a less formal but perhaps more easily understood description is "even-length binary strings where all the 1s are in the first half". If you find that sentence and your description equally communicative (or equally mysterious), that's fine and you can ignore this paragraph.
