In addition to the use and reimagining of existing fairy tales, Chris Colfer added a few 'original stories' to the series. These are told by the twins' father, typically in situations where his children need comfort or advice.
Fanart by Este & Nel
The Curvy tree[1]
Story about a tree that was different from all other trees, which ended up saving it from being chopped down. The twins eventually stumble upon this tree in the Northern Kingdom[2]. (Go here for the Curvy Tree as a Place in the Land of Stories)
Moral: "Being different may be the best thing about you."
"A tiny smile grew on Alex's face. "I think I get what you're trying to tell me, Daddy," she said. -"I'm glad," said Mr. Bailey. "Now all you have to do is wait for the loggers to chop down all your peers."
The version by the (fictional) Brothers Grimm from the time capsule in A Grimm Warning can be found in TLOS III, ch 5, p. 100-101.
The Walking Fish[3]
Story about a fish making friends with a boy and wishing for legs so he could play with him on land. His wish is granted by a fairy. When the boy falls into the water, the fish cannot save him because he now has legs instead of fins and the boy dies. The twins eventually meet the Walking Fish[4], named Fisher, who is kept as a pet by the fairy Coral.
Moral: "Be careful what you wish for."
"Dad, that's a horrible story," [Conner] said. How does a boy live by a lake and not know how to swim? Dogs can swim! Couldn't one of them have saved him? Where was that fairy when the boy was drowning?" - "I think you're missing the point of the story," Mr. Bailey said."
The version by the (fictional) Brothers Grimm from the time capsule in A Grimm Warning can be found in TLOS III, ch 5, p. 102-103.