Would the minis for all versions of MLP be Discords, or would they be something that matched their generation? If different, would it match the setting, or the setting that the character comes from?

…either by the coordinators of the continuum-specific OFU or (if no such OFU exists) by the first person to write a mission for that continuum, as stated on the Mini wiki page. How "iconic" the mini turns out to be is ultimately depends on the person creating it.

In the case you've given regarding mini-dragons, I would argue for misspellings creating either a non-descript dragon or a dragon with a power somehow connected to whatever was misspelled. I would also argue that mini-dragons are a little generic, especially since there are also multiple canons that use mini-dragons or dragon-like creatures. But like I said before, it's up to the person creating it.

For example (quoting the wiki), Avatar: the Last Airbender/Avatar: Legend of Korra minis vary depending on the nation of the misspelling. Air Nomads create mini-Sky Bisons, Water Tribals create mini-Unagi, Earth Kingdom subjects create mini-Badgermoles, Fire Nationals create mini-Fire Dragons, and Republic City-related people and events create mini-Fire Ferrets. Unaffiliated or miscellaneous minis take the form of mini-Flying Lemurs, and all minis default to this form when sent to the Official Fanfiction University of Avatar: the Last Airbender.

I noticed in some instances, like in a fantasy universe, that the mini is the first monster encountered (God knows I wouldn't choose a Fury for the PJO continuum... Can we change that?).

In others it's simply a miniature version of the character or item in question.

Others may even be an important character (Mini-Roots? Who cam up with that for the Artemis Fowl continuum) or iconic item.