Let $T\subset G$ be the set of all torsion elements in a finitely generated infinite group $G$, and let $B_n\subset G$ be the closed ball of radius $n$ around $1$ w.r.t. to the word metric for some choice of a finite generating set. Consider the upper density $$ t(G)=\limsup_{n\rightarrow\infty}\frac{|B_n\cap T|}{|B_n|}. $$ The extreme values $t=0$ and $t=1$ are attained trivially for (torsion-)free groups and finitely generated infinite torsion groups respectively. Slightly less obvious is that $t(G\ast H)=0$ whenever $t(G)=0$ and $H$ is finite, which one can show using Kurosh's Theorem.

Questions

1. Is the value of $t$ independent of the choice of a generating set for $G$?
2. Is the $\limsup$ always a proper limit?
3. What is known about the values $t\in[0,1]$ that occur?