1. I'll help (and will volunteer to be available as a judge if needed for most of the contests).
2. I second Littha's suggestion we requisition a Homebrew sub-forum (could simply be Homebrew Min/Max Contests)
3. This would vary by the contest, I would think. For instance, many could, as Littha says, use level 10 and 20 builds. An E6 contest could not. If we're also using this to gather homebrew feedback, we might consult the homebrew authors, who might have specific areas they could use targeted/tested, like "level 13 builds," if a new game element comes into play at level 13 that they're concerned about.
4. I would say three judges total: the author and two others. It prevents a tie.
5. Definitely don't allow edits mid-contest. To prevent cases where one submission/entry is seen and subsequently copied by just about everyone (with minor tweaks) because it's clear no other concept will beat it, submissions could be sent in via e-mail to a shared account, or PM'd and then redistributed/forwarded to the other judges. This way the submissions will present a wider array as they will remain private and thus not affect other contestants' submissions.
6. I'd say, run the whole gamut. There might be a class to test, or maybe a feat, or it might be a matter of testing a martial discipline; but there might also be whole systems, and those shouldn't be discouraged. Veekie's list is pretty thorough (with the class addition).
7. Definitely keep a record of previous winners, and include it in each contest (spoiler-blocked for the sake of space, maybe with a recap of just the previous contest and its winner in the main body of the post). As far as things like custom titles, we'd have to consult the Mods and Admins. This part seems less important. If the contests are fun, no one should be complaining.