Let $G$ be a group, say finitely presented as $\langle x_1,\ldots,x_k|r_1,\ldots,r_\ell\rangle$. Fix $n\geq 1$ a natural number. Then there exists a scheme $V_G(n)$ contained in $GL(n)^k$ given by the relations. This scheme parameterizes $n$ dimensional representations of $G$.

Now, I've known this scheme since I first started learning algebraic geometry (one of the first examples shown to me of an algebraic set was $V_{S_3}(2)$) but I've never found a good reference for this. So my first question is:

Is there a good reference for the geometry of schemes of representations?

Now, I have some much more specific questions. The main one being a point I'd been wondering about idly and tangentially since reading about some open problems related to the Calogero-Moser Integrable System:

Are there natural conditions on $G$ that will guarantee that $V_G(n)$ be smooth? Reduced? Now, this is on the affine variety, I know that the projective closure will generally be singular, but in the case of $V_{S_3}(2)$, I know that the affine variety defined above is actually smooth, of four irreducible components.

Finally, for any $G$ and $n$, we have $V_G(n)\subset V_G(n+1)$ (By taking the subscheme where the extra row and column are zeros, except on the diagonal, where it is 1). We can take the limit and get an ind-scheme, $V_G$. What is the relationship between $V_G$ and the category $Rep(G)$? Can the latter be realized as a category of sheaves on the former? I know nothing here, and as I said, most of these questions are the result of idle speculation while reading about something else.

Edit: It occurs to me that as defined, $V_G(n)$ and $V_G$ may not be invariants of $G$, but really of the presentation. So two things to add: one, $V_G(n)$ is intended to really be the scheme $Hom(G,GL(n))$ (there's some issues I want to sweep under the rug with finitely generated infinite groups here, which is part of why I was thinking in presentations), and second, the situations that I'm thinking of are often the data of group with a presentation, so for that situation, $V_G(n)$ as defined should be good enough.