Let $G$ be a finitely generated pro-$p$ group. Let $T$ be the set of all torsion elements in $G$.

- Is it possible for $T$ to be a non-closed subgroup?

Anyway,

- Can $G/\overline{\langle T\rangle}$ have torsion?

For any finitely generated abelian (more generally, powerful) pro-$p$ group $G$, I know that 1. and 2. have negative answers: $T$ is finite and $G/T$ is torsion-free.

Thanks.