Do morphisms of algebraic groups have any special properties? I am mainly interested in morphisms between algebraic groups preserving the group structure; but I am also interested in arbitrary morphisms between algebraic groups. For example,

What can be said about the morphism $x^n: G \rightarrow G$, $x$ goes into $x^n$: is it necessary proper? finite? when is it étale? what if $G$ is commutative but not necessarily an abelian variety?

In fact, I am rather looking for a reference which describes such properties in full generality: that is, between arbitrary (finite dimensional), possibly commutative, algebraic groups in arbitrary characteristic.