1) There are no 'monster knowledge' skills. So unless the players metagame from reading the monster manual or have already encountered a type of creature. There isn't anyway of knowing anything about them. How they act. What they can do. What they are resistant to. What they are vulnerable to. Etc... Is that right? That seems to be assuming the PC's are pretty damn stupid. So our group has just found there is a ghost in our house and are pretty much stuck just trying things at random to get rid of it. Because there is no way to know anything about them?!?
The section on Intelligence in using ability scores gives a few examples of how you can do this: Arcana for the inhabitants of the other planes; Nature for plants and animals. It's really left to the DM adjudication though.
Here's a handy scheme I like to use:
Arcana: Aberrations, Constructs, Elementals, (Celestials, Fiends)
History: Dragons, Humanoids, Monstrosities
Nature: Beasts, Plants, Fey, Oozes
Religion: (Celestials, Fiends), Undead
As you can see by the Celestials and Fiends being in two categories, I can be generous on which skills apply to which, and might allow another to apply on a case by case basis.
I also allow characters without the appropriate skill to make their Intelligence check with proficiency if they know the creature's racial language. If their character's background (lowercase "b", but their "Background" informs that) would indicate they should have knowledge of the subject matter, that would also play into it.
And of course, you also get to set whatever DC makes sense to you. Isn't it great?
