Branch loci of Ramified covers 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.
 A: 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 $\pi_1(X)=\{1\}$.
A: The branch locus in $Y$ need not be a normal crossings divisor even when $Y$ is a projective space. Suppose $X$ is a smooth complex projective surface with non-abelian fundamental group. By Noether normalization we can find a finite morphsim $f : X \to \mathbb{P}^{2}$. The branch locus $B \subset \mathbb{P}^{2}$ will be a divisor by the Zariski-Nagata purity theorem but this divisor can never be normal crossings. If it was, then the fundamental group $\pi_{1}(\mathbb{P}^{2}-B)$ will be abelian by Fulton's nodal curve theorem. Since $\pi_{1}(X-f^{-1}(B)) \subset \pi_{1}(\mathbb{P}^{2}-B)$ is of finite index, and $\pi_{1}(X-f^{-1}(B))$ surjects onto $\pi_{1}(X)$ e.g. by the Fulton-Lazarsfeld connectedness theorem, it will follow that $\pi_{1}(X)$ is abelian which is a contradiction. In general the only implication of the smoothness will be the purity of branch loci: the branch locus has to be of pure dimension one.
