19.2582 -- Research Solution

Known trivia answers:

According to the song, "it comes in a cup" and "it's only a buck".
Chocolate Pudding from the song of the same name by the Mighty Mighty Bosstones

According to the Courier, what Mama was asked to do, in "1776"
Look sharp

Album featuring "On My Way to Paradise"
Butterfly Kisses (Shades of Grace) by Bob Carlisle

Band who did the album "We'll Always Have Ohio"
Little John

BATES will rent you one
?

Beth, who's half kender, half other stuff
Pageturner. Half-kender are from Dragonlance, a Dungeons and Dragons game series and novel series; Beth is mentioned here.

Bob Fitch, Roy Straigis, Mike Brown, and Bill Augustine, collectively
? They were musicians, perhaps composers, but I don't see that they ever worked together

Book whose subtitle is "Creating Virtual Worlds with REND386"
Playing God

Disco or Magnet
?

Dominique Maillet reviewed it in Premiere (France) in July 1984 (pg. 8)
The NeverEnding Story/L'Histoire sans fin? It was a magazine for movie reviews. I couldn't find the contents of the issue online, but this page shows the cover for the issue, number 88, which features Dune at the top, but since that movie wasn't released until December 1984, it must have just been about them making it. The other article featured on the cover is an interview with Catherine Deneuve, which was on page 41 of the issue. So this didn't help. But here we can read an article from a 2023 issue of the magazine which quotes her review of the movie, and this movie premiered July 20, 1984 so is in the right time frame, so maybe.

Eleanor's replacement on a 70's sitcom
Jack Tripper. This is the plot of the beginning of Three's Company.

"Electric Earthquake" hero
Superman

English name of 1996 Stefan Dorra game where "money plays no part"
Black Market (German name Schwarzmarkt)

Fermin Velez's sponsor
Old Navy. He was an Indy car driver and had various sponsors. At the June 7, 1997 race at Texas Motor Speedway, Old Navy was one of them.

Film where Jane Fonda had a body double for her sex scene with Jon Voight
Coming Home (1978)

Film with the quote "Don't you have the whole world to save?"
Mississippi Burning

First song on "Jump Up"
"Dear John" (album by Elton John)

Hollywood Joe's CD combining swing/jazz with rockabilly
Jack of Hearts (1995) is most likely the one intended.

Item A115 at Fatboyz Candy
chocolate kisses. I'm assuming this was a local store that existed at the time of the hunt (or maybe a vending machine on campus) but I can't find any trace of it. This answer makes sense for the question and links other answers in a manner that becomes obvious when you have enough of the answers.

It features The Seven Arits (with "the")
Papyrus of Ani or (Egyptian) Book of the Dead

Its tag line was "Intelligence runs in the family"
PalmPilot

"Key" of "Duet for Human and Narn" in a 1996 comic book
C Sharp. A Babylon 5 comic book from 1995.

Kombinatie tekenfilm/live action lijkt nergens op behalve op Neverending Story (with "The")
? This one is written in Dutch; it says "Combination cartoon/live action not like anything but Neverending Story." So possibly the Dutch title for it, except that I don't see that NeverEnding Story has a cartoon portion (despite the drawings used in some advertising for the film).

Laserdisc number 5720, catalogue number ID 2424 LI
Three of Hearts (See here)

Madonna fan page: "Something's ___"
Coming over (a lyric from her 1994 song "Secret")

Montag's activity in a 1966 film
Book burning (he's the lead character in Fahrenheit 451)

Movie featuring the expression "Christopher Columbus!"
Little Women

Movie featuring the line "You're a very paranoid person. I like that."
Dear God

Musical whose prologue features Frannie and Manny
?

Name of "storage building" number 20 at UMD
Motorcycle (Here you can see it labeled 020 Motorcycle Storage Building)

NASDAQ ticker symbol of group headquartered at 4200 Parliament Place, Lanham, MD
CNET. This is tough, as it's a shared office building housing many companies, but by searching for NASDAQ along with the address, I found this 1996 filing which shows COMNET Corporation, traded as CNET on NASDAQ, was headquartered here. (It looks like their subsidiary Group 1 Software trading as GSOF was also headquartered there, but CNET fits in the puzzle.)

1942 Hopalong Cassidy western
Undercover Man (The other possibility was Lost Canyon)

November 2 in Mexico
Day of the Dead

Peruse
look over

Rubbing oil sold by I. Armstrong
?

Song featured on CD5 single: Arista 74321-19619-2 (UK), 1994
"In the Navy" (the Village People song)

The domain name of HuskyLabs
butterfly.net

The Irish version requires fresh pig's blood and beef casings
Black pudding

"Trzy kobiety"
Three women? It's Polish for that phrase and is the title of multiple movies and books.

What Mabel is doing when not listening to music or riding her bicycle
?

Where Tim Wilson claimed the Yeagre was on September 15, 1997
?

Verse described on pg. 54-56 of More of Paul Harvey's The Rest of the Story
"Old King Cole"

Putting it Together

We are making chains of phrases where either the first part or the last part is the same between two consecutive phrases (bold parts unattached):

And we have these unlinked answers and 9 unsolved ones:
The final answer, NAT, goes in place of old in old king cole, and page in pageturner to make two more unclued phrases. I assume all the phrases were meant to form a loop if the two phrases with NAT were added.

I don't see clues matching them, but "day tripper" and either supermarket or "in the market" could tie together some of the pieces we have. very tenuously we may have two different versions of the title of The NeverEnding Story.