Let $F_n$ be a free group of rank $n$. Let $w\in F_n$ be cyclically reduced.

What can be said about the element(s) of minimal length from the $\textit{ncl}(w)$ (normal closure of $w$ in $F_n$)? Under what conditions is it a trivial normal root of $w$ (i.e. is conjugate to $w^{\pm 1}$) ?

Let $v, w\in F_n$ be cyclically reduced. What can be said about the element(s) of minimal length in $\textit{ncl}(w)\cap \textit{ncl}(v)$? Under what conditions is it a conjugate of $\[ v, w \]$?