ok, looking at the list here we go:
1. No OneNote does not send reminders
2. you can not set any kind of reading rights per section and users. you either grand read only rights or can edit rights
3. Yes but you have to do it manually
4. No it will creat a task which can be added to outlook, via tagging you can set a due flag. However monitoring goes via outlook
5. adding tags - yes
6. subtasks - no
7. write notes to tasks - yes
8. reminder for tasks - no
9. sorting, prioritizing - all manually
10. follow task - via outlook
11. and 12. via OneNote mobile - password protect section.

Looking at the list o think Outlook tasks would do exactly what you are lookimg for.