[Lizard]

I'm not familiar with OneNote, but it seems like you might be able to get a lot of this functionality in OmniOutliner?

1) you can organize all your notes in an outline. the top levels of the outline are available in the drawer to the left.
2) not explicitly, but you could add a "Tags" column, or just put keywords in the notes field of any row and then search for them.
3) Yes
4) Yes, especially lists and styles
5) Yes
6) Yes
7) HTML, PDF, no particular "sharing" features, though.

If you've looked at OmniOutliner and it doesn't do what you want, please make it clearer what features it would need.