If I wrote a character saying there are evil creatures beyond the forest, for example, does it necessarily have to be true? The character clearly believes there are, and there could, in the context of the story, but lets say there isn't; am I breaking the Chekhov's Gun writing convention?
That depends on how it's presented. You can say that a room has plush carpeting and never have it play a relevant part in the plot without breaking the convention, but you can't have a character who has a terrible phobia of full piled flooring and the room with the carpet and not break Chekhov's Gun rule if the two never meet. Evil creatures are one of those things that it would seem like you would be breaking the rules if you didn't get them involved in the plot, but if you used them solely as a descriptive to either the world or a character, then I really don't think you would be. But whether you are or not, does it really matter?
No, that's not Chekhov's gun. Chekhov's gun is something totally different. It's all about how if you show something to the audience then it has to be used in some way. As long as your monsters are a plot point in the story, whether real or not, then it's not Chekhov's gun. The only way it could be is if you write in the early story about the monsters and how people believe in them and then it's a story that never discovers if the monsters are real or not, or doesn't involve that myth in any way. Chekhov's gun in this context would be "Man, those monsters... Super scary. Better keep away from the forest. And now off to adventure by the river and in the caves and never go near the forest."
Ah, that makes sense. Here's some context: The characters in my story are deeply religious and I figure religious people are often superstitious. If there is an area that people avoid, often because it's naturally dangerous, like a bog, there's often legends involved about evil creatures so that children avoid going there. The main character finds the whole thing intriguing and chooses to believe the stories but the creatures are never seen. He forgets about the stories when he grows up but look fondly on it later. The monsters are mainly used to creating atmosphere and dread from a young kids point of view.
The only thing I'd add is to avoid piling on a bunch of red herrings, then having one of them turn out to be the truth. The Execution Channel, by Ken MacLeod, is a prime offender in this: A number of cities around the world just suddenly become craters overnight, and he throws possible explanations for why at the reader in the form of (it's been a decade since I read it, and I didn't like it, so some of the following may be incorrect) blog posts, newspaper stories, bar conversations, speeches by heads of state, yadda yadda until finally one of the apparently minor and less believable ones is revealed to be the truth. Not so much Chekov's gun as Chekov's whole gun cabinet, knife rack, and junk drawer and by the way, the murder weapon was a butterknife....
Yes, that's a good point. Chekhov's gun doesn't have to be literally fired, it can be a misdirection, it can be a twist or all kinds of things but you have to play fair with the audience on this stuff. If the gun is lost in the clutter then you've almost done a deus ex machina; your foreshadowing was unsuccessful enough that it may as well not have happened.
Hands down my favorite use of Chekhov's gun and the most original deployment in my opinion is from Jim Jarmusch's Only Lovers Left Alive. Spoiler warning. In the beginning of the movie, Adam has a bullet made from a specific type of wood. He has suicide on the brain and when a young vampire shows up and kills his best friend you think the bullet has her name on it. It doesn't. In the final act, he and Eve are in Tangie, slowly dying of blood starvation. EVE buys him an instrument that turns out to be made from the same kind of wood as the bullet in the beginning. So rather than being the bullet that kills him, it does the reverse by giving him a reason to continue living.
*nods* Yeah that's a nice inversion. And it underlines the message behind the rule; it's not that you have to actually fire anything, just if you show us something you have to have a reason to do it.