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Moderators cannot see the identity of anonymous people. The only people who can do that are admins. The only difference between mods and non-mods are how mods can hide posts and how mods see an "all mytake section" / "reported posts" section.
Likewise, while mods can "hide posts," they can't remove em. Mods just send em up to admins who decide whether or not to remove/reinstate them.
For the list of mods, check out the FAQ