Da Boss, we don't have a lot of hard and fast rules. Basically, you cannot write about a ship, character, species, weapon, planet, etc. that we haven't already used. The famous ship is off limits. We have it in the list of ships that exist, but her adventures are so well documented, we don't see a need to explore them. (Besides, it is outside of our license!

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So no scenarios, no fiction, and no RPGing may include the characters. The assorted comics, novels, movies, and later series are not in our license. So there's no bat'leth in our art or fiction, for example. Our Klingons and Subject Races have various blades, but not that particular one.
The Mirror Universe wasn't in the SFU; it cannot be used. We have played with a Reflection Universe, but that is one that SVC would need to run past the lawyers first prior to publication.
Burger, let's not go there. That's one of those "we could probably win, but the court costs would be too high" battles. Never start a battle you don't have to (or cannot) win. There are lots of people and ships in the SFU to write about.
The Kzintis are used with permission of Larry Niven, but they are not his Kzintis. Ours are bipedal tigers and if you ever thought that one of their females were not sapient, she'd disabuse you of that notion so fast that your head would be spinning after her "love tap." We never, ever abbreviate Kzintis as "Kzin" as that is not what our Tigermen are known as. Do they eat their foes? They certainly have that reputation and there are rumors of a specialty book titled "How to Serve Hydrans" and it isn't for those who "buttle." :shock:
For the Romulan, the artwork posted isn't ours and is under copyright, I suspect, so we'd probably remove the link were it on our board after verifying the information. SVC and I (as do most publishers) feel very strongly about copyright as we spend time each week quashing pirates of our books.
Does this help you on your questions?