1) There is just no telling how long it will take. It depends on the independent decisions of volunteer editors. From outside, the process looks random. From inside, it just looks indeterministic.
2) No, there is no notification of any kind. If the submittal has a problem, it'll be fixed if possible, otherwise just dumped silently. A significant minority of submittals (a few percent) have irreparable problems. No problem -- so do a significant minority of links from search engines and other sources.
As for the website noted in the submittal: if it conforms to the ODP policies (that is, contributes to its mission), even then editors will ignore problems if possible.
But if the website isn't considered worth listing, it's certainly not worth opening yourself up via e-mail with a possibly irate webmaster! No, there would not be any notification.