Wow, and I was just randomly guessing.
Clues:
- Not a human
- He was in a place of which its name was a tribute to a movie special effects pioneer.
This should be uber easy.
~ Flare
WALL-E - Ben Burtt. 
Erm, not the person I was thinking of… Maybe I should add another clue.
- Not a human
- He was in a place of which its name was a tribute to a movie special effects pioneer.
- He’s not in WALL-E
~ Flare
OMG, i really, really think it’s WALL-E. lol
ermm…Buzz Lightyear?
lol Pizza Planet is not a person’s name, as far as I know. 
It’s not Buzz.
Since I’ve added another clue an answer ago, the next one will be 4 answers away.
~ Flare
Let’s see,
1. NOT human,
2. In a place named after a famous special-effects pioneer,
3. NOT in WALL-E,
Gotta be one of the Monsters, Inc. characters then, but there were a bunch of monsters there at Harryhausen’s, including two of the main characters. I’m gonna go out on a limb and say Mike Wazowski here, although it could be Sulley, or that octopus-like Sushi chef.
OK, first clue to my character:
1. He wears what some would consider “punk” or “Goth jewelry”.
pitbulllady
Okay, thanks for the courtesy of waiting for my confirmation first. 
Yeah, it’s Mike. Congrats.
~ Flare
pitbulllady: Violet?
– wannabechef91
Nope, it’s not Violet, although she’s probably the first Pixar character people think of when they see the word, “Goth”.
OK, next clue:
2. This character is REALLY fast and hyper.
pitbulllady
Syndrome?
Nope, not Syndrome, either(can’t recall any jewelry or the like on him, actually).
Next clue:
3. He REALLY hates dolphins!
pitbulllady
OOOH! I KNOW! IT’S SID!
I feel good about that answer!
Nope, not Sid, either, though Sid does strike me as the sort of kid who’d claim to hate dolphins, bunnies and other critters most people think are cute just to annoy everyone else. I don’t recall him specifically saying so, though.
Fourth and last clue:
This character is NOT human.
pitbulllady
Oh! it’s one of Bruce’s shark friends, “They think they’re SO CUTE”, “Oh, look, I’m a dolphin! Lemme flip for you!” Yeah! They have fish hooks and crap in them. I don’t remember the the other sharks having names. If you’re looking for a name, I’d probably just go with Bruce, but it was one of his friends.
EDIT: Oh wait, I found his name, it’s Chum!
Double EDIT: Crap, it’s Mako, Mako hates dolphins, he’s the hammerhead
Yep, that’s him! He’s a Mako shark, but his name is “Chum”. “Anchor” is the Hammerhead, but Chum is the who who has issues with dolphins, lol. He’s also got that big fishhook through his snout. A friend of mine, who’s into reptiles, wears a fishhook through his nose, and he’s pretty much a Goth, so that’s where I got the idea of the fishhook being a Punk or Goth fashion accessory.
pitbulllady
Yeah, yeah, that’s it.
Ok, ok, I’ll try this time.
Clue 1: He causes a major plot change, but is only in the movie briefly
random guess: Carl?
Um, only in the movie briefly? lol, I don’t blame you for saying Carl though, he’s my favorite character,…
Clue 2: He doesn’t have any lines.
I’m making this one really tough, being as vague as possible.
BURN-E.
whoa. this quite tough…WALL-E?