1. Yes. They will become full members of the organization. Joining an organization allows the admin of the organization to have full control over the member's content. Thus, if the person wants to maintain personal content, they shouldn't join with their public account. Also, if they want to leave the organization, their account username is deleted.
2. No. Organizational accounts can't join groups owned by Public accounts and vice versa.
3. No. Public accounts can't join organizational groups. They can, however, see organizational groups that are public and where all content in the group is shared publicly.
thanks,
Mike