Create Facebook with Wordpress (not visually, mentally)

I want to create a site like Facebook :slight_smile: But requirements are restricted to compare with Facebook.

1- User has only one account
2- User can create a Fan Page or is assigned to role on a Fan Page (admin)
3- Fan Page's admin can invite other users
4- The Users can join Fan Page without/with permission (optional)
5- Fan Page's member can create Posts on that Page
6- Every Fan Page's post is visible to All Users
7- But only Fan Page's users can see the Fan Page's Post in their wall
8- Not authenticated users see All Activities on the Wall.
9- If there are not enough stories for member on his/her wall then stories are completed with common activities. // This requirement optional because It is not easy I know)

Tools

Buddypress, Wordpress :slight_smile:

First I thought I can use Buddypress's Groups as FanPage but the problem is the User who involves the group could not send post because posts are sent to Categories.
Buddypress's group approach is good for Wall implementation.

I thought to bind Categories to Groups also but I'm a little confused.

Then I thought I can imitate Fan Page via Category.
But there are problems for Category approach also.

I considered MultiSite with MultiDb but single signon and Invitation to FanPage or seeing other FanPage's posts are problematic also?

The Best way seems Category as FanPage approach.
Could you suggest any solution for these requirements?
Which plugins (WPMUDEV's or others) could be used for these requirements?

Thanks.