I like the idea of minis being created as something for the Word World to refer to when the canon name is not correct- in my headcanon, this means that minis will actually perform the action or description that the misspelling is involved in (if such action exceeds the mini's regular capabilities, i.e. a character kisses Rtas Vadummy or Tail'zora pilots a shuttle, it will either demonstrate new powers or do the best it can, then revert to normal immediately afterward).

In terms of where they exist before they're "invoked", probably the same non-place as characters who have yet to be introduced. I usually refer to creating something new in a story as "pulling from the possibility foam".

As for what they eat, they can likely survive on anything that would feed their original creature (or nothing if said creature does not need to eat), but all can also consume a variety of literary materials including punctuation, physical media containing their canon (or other written materials?), and glitter- this last is likely most interesting, as they are uniquely immune to its corrupting properties and will actively eat Sues if given the opportunity.

Okay, so in a Badfic, when a name comes up it refers to something. When the name is misspelled, it doesn't refer to the same thing, so the badfic generates something to recieve the action- a Mini.

Also, Poké-minis are Missingno..

First: Pokemon minis are mini-Missingno, which is a glitch Pokemon from the Generation I games. The page should specify whether a continuum has more than one mini type and what those types are.

Second: I would assume they're a form of energy, too, but you can't safely convert mass into energy (or vice versa) unless you're in Star Trek. Then again, Word Worlds are definitely weird enough to ignore the laws of thermodynamics and physics (temporarily). (The other dimension idea sounds cool)

Third: Technically, as inorganic beings, they don't need to eat. I think they respond to human food, though; I specifically remember that Thomas Greenwall adopted Witmol the mini-Telescreen by using a chocolate bar as a bribe. *shrug*

Pokemon has mini-Missingno.s and mini-Deoxyi (I think that's how you spell that?). Yu-Gi-Oh! minis, for example, take shape of the ace monster of the misspelled character - for example, Yugy Mutou is a mini-Dark Magician, Jooy Wheeler is a mini-Red-Eyes B. Dragon, Yuma Tsukamo is a mini-No. 39: Utopia, etc.
The big rule is: whoever writes the OFU for the particular verse gets to decide about the mini. If there's no OFU around, whoever finds the first mini gets to decide what it's like - for example, I was the first person to find Teletubbies minis, so I decided they're mini-Noo-Noos.
As to where they come from... they come from the same place punctuation showers come from. What they live on depends on the breed. I'm pretty sure mini-Reapers eat temporal paradoxes, and it's known that mini-Balrogs like bacon and eggs. Mm, bacon...

is that minis eat words that are misspelled. That's just my headcannon, though.