BuddyPress.org

1) You can control what is displayed on your home page by manually modifying the home page template.

2) Not sure what you mean here.

3) The bp-default theme has been criticized for throwing all the features of BP at the user. Features can be disabled in the BP admin area, as well as through a custom theme. Test out BuddyPress on the test site – http://testbp.org – see if it fits your needs.