How did the Edo Tensei reanimated Second Mizukage summon the Giant Clam?
He probably summoned the clam the normal way with blood. The anime / manga probably just skipped the summoning scene because this isn't a major character and the panels could be better filled with other scenes.

Edo Tensei reanimated characters do in fact have blood. I believe there are a few examples, but the only one that comes to mind at the moment is Itachi's eyes bleeding after using Amaterasu.