Sir Rhosis, “behind the scenes” questions are certainly allowed - even encouraged, if not too obscure!
Khan, as to question 4, yes, I was thinking of the USS Rhode Island from VGR “Endgame.”
Numbering, Trekkers, numbering! Khan 's k1-k5 would be #25-29. Doc Cathode’s DC1-DC3 would be #30-32. Khan’s subsequent k6-k10 would be #33-37. The next posted question should be #38.
Answer to k3 (aka 27): Marc Alaimo played Gul Macet on TNG’s “The Wounded.” Salome Jens played the Preserver hologram in TNG’s “The Chase.”
How does former Los Angelese Police Department Lieutenant Wilbur Clingan figure into Star Trek lore?
Name the final episodes which had these original story or first draft titles:
a. The Day Charlie Became God
b. The Paleface
c. The Last Gunfight
d. The Unreal McCoy
Sir Rhosis
Shadow Of The Gun
Marc Alaimo (Dukat) previously played another Cardassian commander, in one of the earlier appearances of Cardassians in TNG – he played Gul Macet. I think he had some other guest roles as well, but that’s the one that I remember well – playing a different Cardassian before he was Dukat. I remember at the time hearing it like one word – “Golmacet” – before I later saw it written and realized that “Gul” was a title.
Close enough, Doc, but actually, “Spectre of The Gun.”
I always make that mistake.
I’m pretty sure I know the episodes for the rest, but not their titles.
Do you have to get all four to have answered one question correctly?
I’d say you’re right, but you already knew that. 
Clingan = Klingon
Beside the Wormhole? 
Damn, all I can remember is the look she gave Bashir, and the the invitation to her medical at 1900. Whatley? Watley? She’s a lieutenant at any rate, isn’t she?
k6/33 - I’ll rephrase. In what region of the Bajoran System is the wormhole located?
k7/34 - Close enough. It was Watley. I wouldn’t mind a physical from her either 
39 d. “The Man Trap”
That one where Kirk is adopted into an Indian tribe on an alien planet?
The Paradise Syndrome, I think.
40) What is the combination to Kirk’s safe? (The correct answer can be expressed in three words)
Seeing as how I appear to be stricken with insomnia, here are some booze-themed questions:
41.) What liquor was popular during Kirk’s time that had a distinctive curved-neck bottle that Quark also keeps in stock?
42.) What Cardassian liquor was an acquired taste that Damar was particularly fond of?
43.) What real-life product was used as the “prop” for the answer to 42?
44.) Name an officer who was among the few in Starfleet never to have tried Romulan Ale.
45.) What cocktail did Data prepare for Deanna Troi after she beat him in a game of 3D chess?
You’re right. The episode was TNG “The Wounded,” and it marked the Cardassians’ first appearance. We also learned a lot about O’Brien’s harrowing wartime experiences in that episode.
And another answer:
Incidentally, the guy who played the warden from The Shawshank Redemption played Captain Maxwell in that episode.
Correct on 33, 41, and 42. I was going to say that it was Donorius, but it turns out it’s Denorius. Close enough anyway.
Marc Alaimo also played a gambler in that episode where Data loses his head.
Minuet likes all kinds of jazz except one. Which one, and why doesn’t she like it?
Riker can’t hit the high note, which is why he doesn’t like that song. No, I don’t know which song, just that he can’t hit the high note.
“Get a life!”
Correct answers to all of mine, and I’d say any a., b., c., etc., question would count individually. I did them a. b., c. d., to save typing.
To follow up on a question I posed, since no one has guessed it. Jimmy Doohan gave Scotty his first name of Montgomery. “Montgomery” was his mother’s maiden name, it was his own middle name, and it was the first name of one of his sons.
Also, the former Lieutenant Clingan, now in his 80s, occasionally appears at L. A. conventions, billed as the original Klingon.
Sir Rhosis
He also played a racist cop in the episode where Sisko is a struggling SF writer in 1950s NYC.