no they cant
yes, with themselves
earthworms are hermaphrodite, and there are always plenty of them.. so yes.
EDIT: thanks for the late edit dude -.-
considering you don't get human hermaphrodites that's kind of a weird question to ask.
there are many different types of hermaphrodites, and many different causes. No, they CANNOT mate with themselves, but depending on the severity/type/cause, some can reproduce.
Some annelid species are hermaphroditic, while others have distinct sexes and both reproduce effectively.
In molluscs some species are begin as small males but eventually mature as larger females. These are sequential hermaphrodites. Other species are simultaneous hermaphrodites. Most terrestrial gastropods are simultaneous hermaphrodites.
Most snails are hermaphrodytes. Also earthworms and certain other primitive animals. However, that's about as far as it goes. Higher species such as lizards, birds and mammals are never true hemaphrodytes. They may have external characteristics and genitalia that are ambiguous in appearance, but they are not true hermaphrodytes. The genitalia of male and female hyenas are so close in appearance that they can easily be confused even by biologists/zoologists unless they are sedated and closely examined. There was a nature program on TV where this was actually done. Despite what the Bible says about Mary being a virgin and giving birth, it is an impossibility. Mary had to be impregnated by a human male. Sorry if that sounds blasphemous, but parthenogenisis does not occur in humans.