1. The book cover or poster must reflect a Trek TV series episode (not "The Wrath of Khan" with the TNG crew);
As long as it's taking an ep or movie from one series into another series it's okay. I said episode mainly from habit, since three of the five series didn't have a movie.
2. The crew used in the artwork must reflect a different Trek TV series (as opposed to a certain 2009 movie, and as opposed to the "New Frontier" crew from the book series);
Hmmm.....good question on the movie. I hadn't really given the 2009 movie any consideration. Is your entry based on using elements from the movie?
I suppose you could use a book crew, I think it'd have less punch, though....although I think that mainly because I don't read the books.
3. The supporting cast used in the artwork must be the original supporting cast from the episode in question (so "Balance of Terror" may feature, say, Avery Brooks but also Mark Lenard).
That is not a requirement, but if you have the photoshop skills to pull it off, I'd love to see it!
So if your intention was to do "Balance of Terror" as it would've been done on DS9, then you could use a Romulan from DS9 as long as it were clear that your entry was a DS9 version of "Balance of Terror". (So if we existed in the universe where this was the case, there'd only be 78 episodes of the original series since "Balance of Terror" was not done as an episode of the original series, and was instead a DS9 episode)
Also, it seems my use of the word "crew" is causing some confusion. Looking back, it's clear that I could've worded it as "create an entry that takes an episode from one series and put's it in another (using a wide variety of formats from book covers, movie poster, t.v. guide cover, etc)". As long as it's clear which episode is being used and which series it's being made a part of.
For example "Doomsday Machine"/TNG". Or "In The Pale Moonlight"/ ENT."
This should open it up to a wide range of art styles since the crew itself need not be present. So to use Solarbaby's entry as an example:
The episode is Classic Trek episode "The Changeling"
The series she chose is Deep Space Nine
If it were a book cover, it would be okay to use the DS9 logo, the episode title and a puddle of goo.
Or you could have a minimalist movie poster that was a silhouette of the 1701 and a Borg cube for "Best Of Both Worlds".
Hopefully this will help.