The 'grue' feeds on intelligent beingsThe grue only attacks/feeds on beings who are sapient (not just sentient). Animals can go about unhindered, as you can see at night where beefalo or rabbits are just sleeping in the open with no light. The pigmen are actually frightened of the dark because they are more intelligent than the average animal and so are a potential target of the grue. Possibly, the 'fear' of sapient beings is more nourishing than that of general animal fear. One reason (other than just gameplay reasons) why pigs aren't actually attacked by the grue could be because the player character is more intelligent than the pigs and so is more appetising, meaning the grue focuses on attacking the player.
Maxwell is actually the devil himselfOr at least the equivalent of the devil in their universe. A lot of instances in the game are pointing to this conclusion. For example when Wilson examines the pitchfork tool.
Maxwell is actually Maxwell's DemonMaxwell's Demon is referenced in Physics as being an entity capable of refuting the second law of thermodynamics. However, in order to do that, it'd need to be able to add and calculate a certain number of particles in a certain area. Therefore, Wilson created a machine that Maxwell was a part of, and everyone in Don't Starve is actually a conciousness that is being used to stop the second law of thermodynamics from taking place. Basically, Maxwell is like the Kyuubey.
Willow and Wendy have Psychic Powers.Willow has pyrokinesis, which is why she's immune to fire, and Wendy is a fledgling medium. They both have white eyes because of this.
How the other characters were pulled into the world of Don't Starve.Assuming Maxwell tricked at least some of them like he did Wilson...