First, the editor guidelines are public, check out
http://dmoz.org/guidelines/ . But adding your own site is not forbidden. I've added several e-texts that I had contributed to some site or another. The important rules are three, one of them implicit: You must not COOL your own site; and you must treat other sites like you treat your own. (That is, joining and adding just your own site, while ignoring or reject other listable sites, is not ethical.)
The implicit rule is that you need to take a "broad" definition of "your" site -- that is, if you contributed significantly to it, or you gain income from it, or you have received income or other valuable considerations from its owner, or you have a personal connection with it or a personal interest in it, then treat it like "your" site.
Can you give your own site as one of the "two or three" on your application?
Yes. I do not recommend it. What I recommend instead is giving three OTHER sites, but listing your own in the affiliations, with a comment like "my own site foo.bar.com, also belongs in this category, with title "Foo Bar Inc." and description "Sells mutant kumquats wholesale and retail throughout northern South Dakota."
We're looking for editors who will care about all the sites in that category, not just their own. And ... sometimes there may be several of "your" sites in a category. Suppose you're a webdesigner in Podunk, New Jersey. You're getting money (or chickens, or turnips, or link excahnges, or whatever the locals use for currency) for developing their websites.
Can you be a good ODP editor for the Podunk category? Yes, easily! Even if you list your sites as soon as you develop them.
And ... if (in addition to the basic technical aspects of editing, like not listing inappropriate sites) you fulfill these criteria, we'd consider you an excellent editor:
(1) You list your competitors' submitted sites before your own.
(2) You make some effort to find relevant sites beyond the submitted sites and your own sites.
(3) An outside editor can't look at the listings and figure out which ones are yours (that is, be fair with the descriptions.)
I submitted an e-text of a literary anthology to an archive site recently. The day after it was published, I went about to add it to the ODP. But it took several hours. First I built a category for one author represented in the anthology, finding in the process another e-text on the same general subject already listed (poorly) in the ODP. Then I moved and double-listed the OTHER e-text (for reasons which aren't relevant here, it was eligible for two listings and mine isn't.) Then I listed mine. And I wish I knew of other sites that had a quarter as much content as those two sites -- I'd list them also.
It took several hours involving quick reviews of over 200 search results and adding a half-dozen other sites. (Local categories generally won't take so much work; your business categories may take more.)
It depends on your business. We find e-tailers and "online middlemen" almost univerally aren't able to be fair -- their only stock in trade is search engine placement, and if they were capable of giving value for value (let alone value for free) they'd be in some other line of work. Businesses or organizations that join and support a "Chamber of Commerce" or "Ministerial Alliance" or "Industrial Association" type organization that, say, publishes a membership directory -- obviously have enough public spirit to help build a online directory. Web developers are often willing to be fair with other web developers; SERP perps are, um, much less often (but still occasionally) able to.
But applications are from persons, not members of groups. For example, There are valued and respected editors who are lawyers, real estate agents, and SEO professionals, despite the noxious reputations so many of their competitors have worked so hard to earn.