Sorry your post got ignored for so long! Here's what I've found with a little bit of research.

This appears to be the most recent Yu-Gi-Oh! OFU, last updated in October:
http://www.fanfiction.net/s/6134663/1/OfficialFanfictionUniversityofYuGiOh
In chapter three, it names mini-Kuribohs (minibohs, as it calls them) as the mini for Yu-Gi-OH!.
http://www.fanfiction.net/s/6134663/3/OfficialFanfictionUniversityofYuGiOh

This does contradict our wiki, which says the mini is the signature monster of the misspelled character's name (which is clunky and complicated, and doesn't address non-dueling characters), but I can't seem to find any mention of this appearing in a mission or OFU anywhere.
http://ppc.wikia.com/wiki/Mini (way down at the bottom)

So, to get back to your original questions, OFUs do not require permission (they once did from Miss Sandman, but she's not active anymore; might still behoove mentioning her in the opening author's note) but it's generally bad form to make a new one for a fandom that already has one.

By extension, the OFU I linked above seems to have created the first specific Yu-Gi-Oh! mini, which generally means that's the one the PPC will adopt. (I did find another, older OFU, but it only mentions minis once as mini-duel monsters, which is too general to be of much help.)

Anyone, am I in the wrong here? Can anyone find the source of the mini type mentioned on our wiki?

Hm, I know there's an entry for it on the Minis page, but past that I don't know.

A mini could probably be a Kuriboh, or (as the page says) the signature monster of whoever's been misspelled.

Dammit, botched up the title...@_@