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...
All of the characters are in the Don't Starve world because of a certain brand of radio and Maxwell's machinations.In the video showing how Wilson ended up in Maxwell's world, a radio gave him "forbidden knowledge" to let him build the device that transported him. Word of God says about the radio: "The radio is a Voxola PR-76, manufactured in 1919 by the Voxola Radio company of Sidney, Ohio. The radio offered revolutionary sound and reception quality for the time, and was promoted by an intense national marketing campaign. Very few units were actually produced, because the factory was destroyed in a fire only days after production began. Voxola founder Robert Wagstaff went missing the night of the fire, and the company declared bankruptcy soon thereafter." Maxwell gave Wagstaff forbidden knowledge so he was able to make an advanced radio. It was shown in the video that the radio is Maxwell's means of communicating out of his dimension, so the marketing campaign was meant to distribute as many of those as possible to give Maxwell more victims to play with. All of the playable characters, Wendy, Wolfgang, Woodie, etc. obtained a radio, which sent them to Maxwell's world. Wagstaff was kidnapped and transported when the fire broke out. It's no coincidence that everyone who finds themselves in this new, dangerous place has a name that begins with W, likely even Maxwell himself.