Sound Editor Douglas Grindstaff was involved in creating the noises made by the tribbles. Producer Gene Roddenberry first showed Grindstaff a tribble prop and they discussed how they should tackle the creation of the different sounds made by the creatures. There had to be sounds for their various moods, such as for a very comfortable tribble as well as a fearful or disapproving tribble, rearing up and away from someone it didn’t like. There also had to be sounds for different quantities of tribbles. “I found a dove ‘coo,’ I flipped the track over, and shaved off part of it with a razor blade,” Grindstaff recollected. “I then made a loop out of it, put it on a variable speed machine, and changed the pitch of it to different frequencies. Then I chose those frequencies I liked the best and decided which ones I would use in each spot. I then went to a screech owl for the sound of the tribble rearing up, took the screech owl and played with it and got variations of it. Then I took a bunch of little balloon sounds, where you’d get a balloon and rub it, and we mixed that with other little squeaky sounds that we had in the library, playing with all these at variable speeds, mixing them and making new sounds out of them, and putting them all together until we came up with the various composite sounds used throughout the whole show.” (The Star Trek Interview Book, p. 236)

https://memory-alpha.fandom.com/wiki/Tribble#Background_information

Regarding the most famous images, what images from Star Trek did you know before you ever watched the series? Or do you know from TNG? The Picard face palm? I don’t even remember which episode that’s from.

There are some scenes that are more parodies, like Captain Pike in the chair. The shot of the Balok puppet is famous, mostly because it’s then final shot of the end credits.

Kirk in the Tribbles is probably the most famous shot. Even more than that, I think that if someone who has never watched any episode of any Star Trek series knows something specific about that plot of any episode of any series, they can probably tell you what Tribbles are.