Properties of resolution of singularities

Question

Let $X$ be a complex algebraic varieties and $\pi:X' \to X$ be a resolution of singularities of $X$. Let $Y$ be a smooth (irreducible) subvariety of $X$. Is $\pi^{-1}(Y)$ smooth and irreducible? What if $Y$ is a hypersurface in $X$?

Answer 1

No to the first question. For example, the minimal resolution of an isolated surface singularity might require replacing the singular point $p$ of $X$ with $\pi^{-1}(p)$ a chain of rational curves. Then $\pi^{-1}(p)$ is reducible and connected, hence singular.