This section describes the characters that make regular appearances (or perhaps have made only one, but could be reused) in Accord Fiction.
When in doubt, ask. That simple, but it's very important. If you think it works with the story, use it. If you aren't sure, ask someone who would be (the person themselves or the fiction coordinator).
Conversely, if you find out someone is writing a story including your avatar, and you want to know more about how you're being used, ask. Individuals reserve the right to ask for changes in their characterization or to ask for their character to be removed from the story. Once it's published, however, it's published, and that's that.
Most of Accord's crew are Terran Human. We have elected for the most part to not go along with Diane Duane's view of a more fully integrated Star Fleet. You should avoid the common fan-boy trap of giving your character lots of special attributes or powers, or some really exotic race, unless you have a good back-story for the character and can think of a good reason why they would want to serve with a human crew.
With respect to Q in particular, it should be noted that Q is quite explicit in TNG: "Encounter at Farpoint" that humanity was simply not interesting enough before that moment to be bothered with. Hence, it's extremely unlikely that even a 'baby' Q would have anything to do with a human crew. The only suspected exception is TOS: "The Squire of Gothos", and that has never been canonically determined.
While there is canonical mention of Trills on Earth as early as the 2240's (DS9:"Trials and Tribble-ations"), they don't seem to be common within Federation territory (TNG:"The Host"). We speculate that, while they might serve as observers within UFP territory, they did not enlist in Star Fleet until the 24th century. Apply to the Fiction Editor if you're interested in making your character a Trill. One caveat against this is that, since Trill are rare in UFP space, there is limited medical knowledge available on them. A post in the New Colonies territories might be contraindicated for Trill.
As for Betazoids, a scene in which Chekov unknowingly plays cards with a Betazoid at the Academy was cut from the shooting script of ST V (and was added to The Fearful Summons by one of ST V's co-scriptors, Denny Martin Flinn). Again, apply to the Fiction Editor if you're interested in making your character a Betazoid.
Regarding Bajorans, nothing canonical is known about the UFP's first contact with the Bajorans. It is known, however, that sometime before the Cardassian occupation, Bajor more or less rejected close ties with the Federation (TNG:"Ensign Ro"); this, combined with the Prime Directive, kept the Federation from intervening when Cardassia invaded. While there is non-canonical precedent for 23rd century Bajorans in Star Fleet (there are two aboard USS Avenger), it's best to stay away from using this species as a template for one's avatar.
Yes, within reason. Tellarites are unlikely to be serving on a mostly human ship for temperament reasons (JC has enough problems, remember...). It is established that most Vulcans prefer to serve with other Vulcans (Spock was considered an oddity for this, among other things), so if your character is Vulcan, there should be a good reason why they've chosen duty with humans.
Also, it has never been canonically settled whether the Alpha Centauri worlds are a human colony or an extraordinarily similar race, so this may be a non-problem. Either way, they're assumed to be similar enough to be able to work together harmoniously.
Deltans are OK, but must be handled with extreme care. The race to which the Saratoga's navigator in The Voyage Home and Federation President in The Undiscovered Country belonged, with all that lovely plumage of theirs, is also OK, because the seem, from what little we can tell, to be psychologically compatible with humans. Some sources assume that these are actually male Deltans (which we otherwise never see on screen), but others call them 'Efrosians'. They have no canonical name.
Probably all right (because they've been canonically seen serving with human crews) are Edoans (Lieutenant Arex from the animated series), the Caitians (Lieutenant M'ress from the animated series). I would personally recommend against any race for which nothing at all is known of their background; for example, several random aliens have been seen in the Trek movies that have never even been named on screen...
Other races will be considered by the Fiction Editor on a case by case basis.
Also, please avoid hybrids. Just because Star Trek makes very bad genetic mistakes all over the place doesn't mean we absolutely have to follow suit. Besides, that angle's been done to death.
You will definitely want to clear it with the player in question, for a whole host of reasons, but otherwise, I don't see why not. As always, the player of a given character reserves the right to veto.
At present, there is only one established non-platonic relationship for any of our player-characters in Accord Fiction: Richard Kinne and Buddha Buck's RL relationship is mirrored into the fiction. Other real-life relationships have not been carried into the fiction, by and large, either because they haven't come up or because the player has chosen to do it that way.
In particular, Commander Shappe (retired) and Major Getty, although married and insanely in love in real life, have a cordial but solely professional relationship in fiction; furthermore, Shappe's one previous RL involvement with a fellow Starfleeter was never carried over into Avenger fiction and therefore is not part of Accord fiction, either (if you don't know what this refers to, you needn't concern yourself).
'Slash' fiction should be avoided. Romance is fine; flirtation is fine; but this is a family program.