Show that language generated by grammar is regular
Prove by backwards complete induction that each $X_i$ generates a regular language (backwards induction means that you first prove it for $X_n$, then for $X_{n-1}$, and so on, until you reach $X_1$; complete induction means that when proving this for $X_i$, you can use the induction hypothesis for all of $X_{i+1},\ldots,X_n$).

Perhaps the easiest way to carry out the inductive proof is to give a regular expression for the language generated by each $X_i$.

The only non-trivial part is handling productions of the form $X \to XY$. Here you need to use Arden's rule, which states that if the only productions having $X$ at the left-hand side are $X \to XY \mid Z$ then
$$ L(X) = L(Z)L(Y)^*, $$
where $L(X)$ is the language generated by $X$.