Let $G$ be a group and $V=Var(G)$ be the variety generated by $G$. Suppose the axiomatic rank of $V$ is $n$. Let $Id(V)$ be the set of all identities of $V$.
1- Can we say that every element of $Id(V)$ is equivalent to some identity of the form $$ w(x_1, \ldots, x_n)\approx 1?$$
2- Let $G$ be finite. Can we prove that the axiomatic rank of $V$ is finite without using the fact that $V$ is finitely based?