It seems creatures using elemental damage are not automatically immune to that damage type since they have an Immunity entry (see Fire Elemental or Hell Hound).
What about poison and disease? The Poison Frog has a poisonous bite but no indication that it's immune to its own or that from other Poison Frogs. The Poison rules do not make any such mention either.
Should I assume two Poison Frogs fighting it out would poison each other with their bites? Also, a Poison Frog biting itself (it's, um, a little crazy) would poison itself?
Abilities of interest: Poison, Disease, Curse, Elemental damage, Petrification
Creatures of interest: Oozes (with acid attacks), Mummy (mummy rot curse), Basilisk/Medusa