Given a smooth curve $C$, denote by $\text{Sym}^d(C)$ its $d$-th symmetric power. Let $\Delta$ be the diagonal subvariety which is defined as the codimension $1$ subvariety that at least two of the points coincide. Let $\text{Sym}^{d-1}(C)$ be the closed variety that its embedding is given by adding some extra fixed point. Let $Z$ be either $\Delta$ or $\text{Sym}^{d-1}(C)$.

Question 1.Is $Z$ an ample divisor?

Question 2.Is there any interesting interpretation of coherent modules/vector bundles on the formal completion of $Z$ in $\text{Sym}^d(C)$?

Edit: Is it true that for $Z=\text{Sym}^{d-1}(C)$, the formal completion is going to be a bundle on $Z$? Is it like completing a zero section of a vector bundle?