1: Suppose $A_3$ is the moduli space of abelian varieties of dimension 3 .Is the union of all one dimension shimura varieties in $A_3$ connected?
Could you be more precise about what you mean by a "Shimura curve" inside $\mathcal{A}_g$? E.g., do you just mean a one-dimensional Shimura subvariety, or do you possibly really want $g = 2$ and are just talking about Shimura curves associated to quaternion algebras over $\mathbb{Q}$? –  Pete L. Clark Jul 29 '10 at 14:36