Let $A$ be a Noetherian local domain ($2$-dimensional if needed) such that its punctured spectrum $U$ is regular, and let $A'$ be the normalization of $A$.

1) Is it possible for $A'$ to have infinitely many maximal ideals? (I know that this is not possible if, say, $A$ is universally Japanese, but I am interested in the general case.)

2) If $A$ is excellent, so that $A'$ has only finitely many maximal ideals $\mathfrak{m}_1, \dotsc, \mathfrak{m}_n$, is the restriction map $\mathrm{Pic}(U) \rightarrow \prod_{i = 1}^n \mathrm{Pic}(U_i)$ injective, where $U_i$ denotes the punctured spectrum of the localization of $A'$ at its $i$-th maximal ideal $\mathfrak{m}_i$?

Partial answers or comments on these questions are very welcome.

EDIT: Thanks to Mr Klutz's insight, the remaining question is 2).