I am sorry, my question is very naive.

Edit: Let us suppose that $V$ is a smooth complex projective variety, and $Y\subset V$ is a smooth divisor and has an ample conormal line bundle.

$\textbf{Question 1:}$ if a contraction of $V$ is a projective variety $V'$ what can be said about the singular points of $V'$? What type of singularities can occur?

$\textbf{Question 2:}$ let us start with a singular projective variety $V'$ of dimension $n$ with at worst isolated singularities, and we suppose that the tangent cone of $V'$ at each of these singular points is an affine cone over a smooth projective hypersurface $Q$ of dimension $n-1$. Am I correct if I say that there exists a resolution $V$ of $V'$ whose exceptional divisors are isomorphic to the $Q$'s and that the conormal bundles are very ample?