As provided in the OP, “You must rely on your memory - you can’t consult any book, watch an episode or a movie, or ask someone else, either in formulating or answering a question.” Maybe I should have specified the Internet, but I think that falls under “ask someone else” for purposes of the contest.
Thanks!
No problem, except for that question, I figured that no being in the known universe besides me would know the answer. OK, maybe Brent Spiner might. And a handful of trainers.
Specifically, an “automated rice-picker.”
Shatner (or his stunt double) split his pants in The Savage Curtain.
The OP wasn’t quite clear, so I am assuming you may ask "behind-the-scenes questions as well.
Where did the “Montgomery” in Montgomery Scott come from? Don’t just name the source, name why the source named the character this.
Who originally wanted to play Ensign Freeman in The Trouble With Tribbles? Why was he rejected for the role?
Name another TOS regular besides Shatner to wear a toupee in the movie-era. In the 60s this other actor still had his own hair (most of the time).
Sir Rhosis
What 5-digit number did Enterprise use to force Reliant to lower shields?
16309
w2: What did Scotty get drunk on in the holodeck? And how did Data describe it?
Aldebaran whiskey. Who do you think gave it to Guinan?
w3: How did Lwaxana save Odo’s life?
As I recall, she cradled his gelatinous form in the hem of her dress.
I will return with my questions later. I have to finish a project by 5.
#23 - David Gerrold, author of the episode. Rejected because he was “too skinny” for a Star Fleet officer.
My recollection of the pants splitting was that it was a stunt double thrown in the corridor by Ricardo Montalban in Space Seed. I suppose there could have been more than one instance of split pants, or I could have misremembered.
I knew David Gerrold was the first part of the answer to 23, but I thought it was because he wasn’t a member of the Screen Actors’ Guild. (Though “too skinny” sounds like something Gerrold might claim.)
k1: Which member of the Federation can’t be told apart by anyone who’s not a member of that species?
k2: We know Jeffrey Combs from his roles as Weyoun, Shran, Liquidator Brunt, FCA, and others, but none of his characters appeared on TNG. What lead role in that series did he audition for?
k3: The actors who played Gul Dukat and the female shapeshifter appeared in various roles in TNG before they appeared on DS9. Name them.
k4: Which one of Phlox’s pets did he use to clear the Xindi neural parasites out of Hoshi’s nervous system?
k5: How many members of Khan’s crew got killed by the Ceti Eels?
IIRC, joining SAG would simply be a matter of 1)showing that you had a paid acting gig lined up, 2)signing up, and 3)paying the dues.
All correct. And Khan 's answers to the rest are also correct.
Benzites. IIRC Only individuals from the same geographic region looked alike. They also require cool little vaporizers to breathe.
You’re right, Doc. I got interested in learning about them after I posted my questions, so I looked them up. I took it to mean that there was only one geostructure on their home planet, but it turns out that I misread. Nice catch.
Incidentally, wouldn’t it have been clever if they’d had the Enterprise B christened with a vintage from the Picard family vineyards? Then again, the intertwined fates of so many generations of space heroes tends to get tiresome. Oh well.
DC1-What song can Ryker not play?
DC2-What do Bajorans do when somebody dies? For how long?
DC3- When exposed to the Manheim Effect, Data violates his programming. What does he do that should be unable to do?
DC1 - Nightbird
DC3 - “guess” My answer is, amusingly, just that. 
Don’t know about the others…but K2 is that he auditioned for the role of Riker.
Does that mean I get to ask some questions now?
As for DC2, I know which episode you’re referring to. “The Next Phase,” where Geordi and Ro accidentally get cloaked in an accident while helping a Romulan scout ship. Damned if I can remember what the Bajoran funeral ritual is.
k6 - Where was Deep Space 9 moved after the Bajoran Wormhole was discovered?
k7 - Apropos of the ordinal for this question, what is the name of the crewmember from the Enterprise in “Trials and Tribble-ations” who Bashir thinks he needs to hook up with in case he’s predestined to become his own grandfather?
k8 - Name 5 of the ships destroyed by the Borg at the battle of Wolf 359. Bonus: how many Starfleet ships were lost there?
k9 - In STIV, what hospital was Chekov taken to after he took a dive off the deck of the “Enterprise?”
k10 - Name the crewmembers of the Enterprise A who carried out the assassination of Chancellor Gorkon.
Nicely done. That does indeed mean that you’re up.
You got the song right. But not this one.
Burke and Samno.