This next quiz is a bit different. For all the questions below, there are descriptors of two characters from different companies who share the same code name (spelled the same way). Name the code name and both companies.  Yes, many of the questions will relate to the Big Two, but not all relate to both of them. In most cases, a clue for a particular version might be too vague, but the clues together should point to one answer. Should the clues point to multiple answers, I reserve the right to add to the clues as this gets pointed out.
 
If the company name has changed since they first appeared with that company, you can use any name used while at that company, or the current name.
 
If the character has been used by multiple companies, you can use any company they’ve been owned by, as long as they’ve used that specific code name with that company. In two cases, use the rule for a specific question.
 
1. One has a magical cape, the other has a syllable that’s a form of a municipality somewhere in their real name.
2. One was a western hero, the other led a country.
3. One could split their body, the other derived her powers from deities.
4. One says their code name to transform, the other is from a mythical land.
5. One has abilities similar to Superman’s at the time they first appeared, the other is a reformed embezzler.
6. One is a double legacy hero (one by birth, one by code name), the other can transform into the substance in their code name.
7. One received their powers through alien means, part of the other’s real name is a word meaning wealth.
8. One is a teen who loves burgers, the other only thought he was a kid.
9. One is a barbarian who normally works in his home dimension, the other is a literally larger than life unfortunate racial stereotype.
10. Who is a kid (later adult) with a magical ring, the other sometimes consumed garbage.
11.  One is a white cowled assassin, the other is also a villain for hire, and much of her costume is green.
12. Two characters, originally from different companies, though one company bought out the other's characters. After that they were retroactively revealed to be part of the same team under the same name, even attending at least one meeting together. Due to the nature of these questions, for the character who changed companies, name their original company.
13. One is a mostly red garbed hero, the other is a villain who was killed in a bar.
14. One died in the form of their code name’s namesake, the other has a legal sounding word as part of their real name.
15. One was featured in more than one “impossible story”, the other ran a detective agency.
16. One has worked for the government, the other is a criminal who tends to wear a bikini-like costume.
17. One was part of a team of similarly themed villains, the other led a team of villains against one of the best known hero teams.
18. One is a villain with a fear based motif, the other is a villain who uses a specific type of bird.
19. One got his powers from a special vitamin, the other has to keep declining his suit’s offer to enter killing mode. The latter company probably owns the former, but hasn’t used them except for a trading card, so use the original comic company for the former.
20. Both characters operate in the future or at least a possible future; one usually works as part of a super-villain team, the other is a hero who had her own series.
 

18 is correct. Obviously the bird used by the Marvel version is a crow.

Both of those are correct, and efforts on my part to avoid the questions all being Marvel and DC. Archie's Superteens were revealed in Life with Archie (second series) to exist on a different Earth, thus explaining why Jughead doesn't transform into Captain Hero during other times when it would be useful to do so. I can't recall if it was ever explicitly stated, but I imagine that like Captain Pureheart he can cloud's people's minds a little. Otherwise the crown and no mask in both identities is a dead giveaway.

The Marvel Jaguar was of course specifically killed at the Bar with No Name. There was actually one in Toronto but it closed down a few years ago.

2, 4, 5, 7, 9, 12, and 14 are correct and the ones I'm looking for. Specifically, the Marvel Cheetah got his powers from a Kree Sentry.

For 17, I'm using this  part of the rules: "Should the clues point to multiple answers, I reserve the right to add to the clues as this gets pointed out." Magneto is technically correct but not what I was looking for, so: For the first character, the theme is corrected to their code name.
 

3. You more or less got this one except for getting the company name wrong. The trick was that when Jerry Ordway was writing Power of Shazam, he had Mary share the Captain Marvel code name with her brother (probably because her usual code name reveals her actual code name). I don't think other writers so much had her change the code name as simply ignored/didn't know about the other code name. Regardless, I deliberately used her to make that one more of a challenge. That being the case, since she didn't use the identity under Fawcett, that part is incorrect due to the final rule paragraph, though obviously that leads to DC.
10 is correct. In fact a careful reading shows that this led to the Marvel version's demise. Scourge got to the institution just after he escaped and therefore Fly should have been long gone. However, he stopped for garbage, which gave Scourge time to catch up to him.
15 is correct,
20 is correct. In some places the DC version uses the hyphen. For example, the looseleaf Who's Who series: Didn't realize that bit about the present with Marvel Spider-Girl, though that does make sense from a crossover standpoint.

6. Correct, though he more directly succeeded the Garrett Sandford version from his perspective, even though he was obviously aware of Dodds. And of course the Marvel version is generally considered to have William Baker as his real name, with Flint Marko a frequent alias.

16 is correct. This is a case where either company would have worked for the Eve Eden version, as IIRC she  worked for the government in both Charlton and DC comics, though only with the Squad under DC.

19 is correct. Not to be confused with archaeologist Dan Garrett who has been used by both Charlton and DC.

The remaining answers (I'll likely revisit this series sooner than later).
1. One has a magical cape, the other has a syllable that’s a form of a municipality somewhere in their real name.
Cat-Man. The DC version (and this appears to be another case where the character can be spelled with or without hyphen) has a cape that some accounts claim give him nine lives. One Marvel version is Townshend Morgan.

11.  One is a white cowled assassin, the other is also a villain for hire, and much of her costume is green.
Enforcer. The Marvel version has a white cowl, and the DC version, at least Mica wears a largely green (and orange) costume.

17. One was part of a team of similarly themed [in terms of code name] villains, the other led a team of villains against one of the best known hero teams.
Libra. For both the human and android versions, the Marvel version is a member of Zodiac. The DC version led the Injustice Gang of the World against the Justice League of America.

Andy E. Nystrom wrote:

This week’s quiz is about animals. Obviously humans are animals, but humans, and humanoid aliens such as Superman and Martian Manhunter are excluded. However, other standard looking animals, extraterrestrials that resemble Earth animals, and anthropomorphic characters all count.

4. What is Hoppy’s heroic alter ego?
5. Who was the first animal superhero to be based on the Flash?
8. Who was Speedball’s cat?
10. Hellcow was steaked, er, staked by whom in the former’s first appearance?
13. What team was Detective Chimp a member of?
17. Which rodent team was arguably the best known of the Teenage Mutant Ninja Turtles swipes?
18. What is the name of Marvel’s team of heroic elephants?
19.  Which animal protagonist was once told he would die alone and unloved?
20. What is the Space Canine Patrol Agents’ chant?
 
 

4. Captain Marvel Bunny
5. The Terrific Whatsit
8. Niels
10. Howard the Duck
13. Shadowpact
17. Adolescent Blackbelt Radioactive Hamsters
18. Power Pachyderms
19. Cerebus the Aardvark

Andy E. Nystrom wrote:

14. Duktor Doom claimed he didn’t want to be a what?
15. Goose Rider first appeared in which series?
16. Which rabbit’s adventures were published by Continuity? 

14. a villain?
15. Marvel Tails?
16. Bucky O'Hare

Andy E. Nystrom wrote:

6. Who were the most prominent members of the Junior Woodchucks, i.e. the ones who had their own title?

Huey, Dewey and Louie, Donald's nephews. But a counter question - can you name the fourth nephew, who appeared intermittently until a story finally confirmed him in canon (even if later ones try to ignore that)?

Andy E. Nystrom wrote:

7. Who was the original Ka-Zar’s animal companion?

Zar, the lion. Ka-Zar in the original's instance meant "brother of the lion." Which presumably means Zar's name is either "Lion" or "brother."

Andy E. Nystrom wrote:

11. The Phantom Blot often battled which superhero?

Supergoof.

Andy E. Nystrom wrote:

12. Which Rocket Raccoon ally resembles a walrus?

He doesn't resemble one, he is one. Wal Russ.

Andy E. Nystrom wrote:

13. What team was Detective Chimp a member of?

I know Shadowpact is already mentioned, but he was also in the Mystery Analysts of Gotham. Yes, I know that's from Scooby-Doo and Batman: The Brave and the Bold, but you never specified which reality you were asking about. And also Justice League Dark.

 

Andy E. Nystrom wrote:

13. I'll take your word for those. I haven't read the Hanna-Barbera crossovers and I know little of the DC Universe after August of 2011.

The Scooby Doo/Batman one is a movie, and well worth seeking out if you've not seen it.

Andy E. Nystrom wrote:

Loki wrote:

The Scooby Doo/Batman one is a movie, and well worth seeking out if you've not seen it.

I might see it at some point. I think now I've seen it in stores but didn't pick it up because I couldn't get into the main series. Would you recommend it to people who like the characters but couldn't get into the B&B TV series?

If you didn't like the B&B TV series, then possibly not. 

9. I think Pig-Iron's alter ego, Peter Porkchop (?), appeared first.

2. And I really hope the answer isn't "Kyle Raynor."  18 years of Dan Didio's war against legacy characters was 18 years too many.

Andy E. Nystrom wrote:

Forgot to call a day's notice yesterday so you get an extra day on the remaining answers:
2. Who more or less ousted a Green Lantern out of their own title?

Streak the Wonder Dog.