TITLE: Branch loci of Ramified covers
QUESTION [9 upvotes]: Let $X\to Y$ be a $d:1$ ramified covering map from a smooth complex projective variety $X$ to a smooth complex projective variety $Y$.

Question 1. What does the smoothness imply on the branch locus in $X$ or its image in $Y$?
  Does it imply that its a normal crossing?
Question 2. If not, assuming $Y=\mathbb{P}^n$, can we always deform $X$ to get a normal-crossing branch locus in $\mathbb{P}^n$ (or at least for its preimage in $X$)?

Comment 1. Regarding the nice answer of Tony, you may assume $X$ is simply-connected.
Comment 2. By normal crossing, I mean the reduced branch locus to be normal crossing.

REPLY [8 votes]: Even in the simply connected case there is no hope. 
Let $X$ be a smooth cubic surface in $\mathbb{P}^3$ and take a general projection $f\colon X \to \mathbb{P}^2$. Then $f$ is a branched triple cover and it is well known that the branch locus $B \subset \mathbb{P}^2$ is a sextic curve with six ordinary cusps lying on a conic.
There is no way to deform this cover (mantaining $X$ smooth) in order to obtain a branch locus which is normal crossing.
Notice that $X$ is a rational surface, hence $\pi_1(X)=\{1\}$.