Topological properties of etale morphisms abelian varieties

Question

Let $A$, $B$ be abelian varieties defined over $\mathbb{C}$ and $f\colon A\rightarrow B$ be a separable isogeny. Then it is an etale morphism in the sense of scheme theory. However, I am not familiar with scheme theory at all. Is it correct that $f$ has the following properties and how can I prove this?

1. All fibers of $f$ have the same finite cardinality;
2. Considering $f$ as a map of the analytifications of $A$ and $B$, it is a Galois covering map.