A lot of the information in this writing guide applies to fanfiction for any fandom at all. But there are "rules" (aka canon and fanon) that apply to only Cats fanfiction...

Magic: Characters with magic (Macavity, Mistoffelees, Coricopat, Tantomile) are hard to write. Amateur authors always make them way too powerful. Killing with a thought is by far a favorite power to give Macavity and Mistoffelees, but something that devastating should have a consequence to prevent the toms from just using that power on every nuisance that bothers them, or there should be a character trait that makes the conjurer avoid it (Macavity might like to torture his victims, Mistoffelees is just too nice...). That would make the characters "all-powerful", which is BAD. Be careful of the amount of powers and the strength of the powers you give your conjurers.

Macavity's Magic: Huge debate on this one. In canon, Macavity is only gifted with levitation. But it's become fanon (rules that fans make up) that he is a conjurer just like Mistoffelees. Whether you write him as a clever theif (very clever) or a conjurer is up to you.

Mistoffelees' Magic: Another controversial one. The fandom agrees that he IS magical, but the kind of magic is up for debate. In his song, he only does parlor tricks (card tricks, dice tricks, slight-of-hand, etc.). But a lot of people give him other abilities, as well. That's all fine and dandy, if you want, but remember that he's younger and probably doesn't have perfect control over his abilities.

Coricopat and Tantomile's Magic: Again, you don't have to write these twins as being magical. Completely optional. However, if you do, they seem to be more "mystical" than conjurer. Typically, they can see into the future and heal wounds, or have a great knowledge of witchcraft (Tantomile IS the witches' cat, afterall).

Nick-Names: Don't ever use a Jellicles' nick-name anywhere but in dialogue. A lot of authors make the mistake of writing:
"Hey, Deme," Munkus said.
Really, it should be written as Munkustrap, not shortened to Munkus. Same applies to all names. You write formally, which means no slang and no nick-names. However, when your characters are talking, its okay to have them use nicknames and slang. Authors tend to use nick-names outside of dialogue either because they're lazy, or because they try to give a little variety (which is good, just not the way they go about it). Try using descriptions, like "the silver tabby," the "maned tom/maine coone tom," "the scarlet queen," etc. It gives variety, and is often more interesting to read.

However, a few exceptions can be made in some of the longer Jellicle names, simply because authors have done it so often that it's no longer annoying to read. The Jellicles that can (although avoid this as best as possible) have shortened names are Mistoffelees (to Misto), The Rum Tum Tugger (to Tugger or The Tugger), and The Great Rumpus Cat (to Rumpus or Rumpus Cat).

Princess: Many authors call the female kittens princesses, because the adult females are called queens. It does cause a bit of confusion, because readers don't know if the author is making that particular kitten special (treated like a princess) or just using the princess as a label for female kittens. You could use that term if you want, but it's far easier to use "queen-kits" instead because everyone knows what your talking about. And male toms are "tom-kits." Another label for queen-kits, although rarer, is quitten: a combination of kitten and queen. That's more confusing than the princess label, so don't use it.

Accents can be fun once you get the hang of them. Russian Blue cats, for example, are fun to write with a Russian accent. Mungojerrie and Rumpelteazer commonly have Cockney accents, and Skimbleshanks also commonly sports a Scottish one.

Russian accents are by far the easiest in writing; most authors simply replace the W's at the beginning of most words with V's. So a Russian Blue might say "Vhat are you doing?" instead of "What are you doing?" Some authors even replace the -ing at the end of words with -ink, but that's not recommended. It makes words like "doing" into "doink (D-oink)."

Don't attempt them unless you either speak that accent yourself, have a book with an accent that's particularly well done to use as a reference, do extensive research, or hear it all the time. A simple solution is to write the dialogue in plain english, then have "so-and-so said with a thick ____ accent." Example:
"My, what a beautiful morning," Skimbleshanks said with a thick Scottish accent.
Most authors, even experienced writers, either butcher the accent or can not write it consistently. It might be fine, or at least mediocre, at the beginning of the story, but completely different by the end.

Accents are easily written by simply using words that are unique to that accent/dialect. Writing Skimbleshanks with a Scottish accent, for example, you could simply substitute "lass" for queen, "lad," for tom, "bonny" for good/lovely, "tis' for it's, "ye" for you," "ken" for understand or agree, and "wee" for little. Using these substitutions, Skimbleshanks would say, "Tis a bonny morning for a wee bit of a walk with ye, lassie, do ye ken?" By doing a little research into the accent you want to write, you'll find all kinds of words to use; but don't use too many, or your readers won't understand!

Relationships between Jellicles vary from writer to writer. One author might think that Macavity, The Rum Tum Tugger, and Munkustrap are all brothers, while another might believe that Munkustrap and Alonzo are. Some authors believe that Grizabella and Old Deuteronomy are old mates, etc. There are very few rules concerning relationships, in the familial and the romantic sense. Be as creative as you want! Good stories often involve unusual pairings.