It’s just not a core issue with BuddyPress and dives into the customization of BP. Unless someone has specifically needed to do this in the past no one will be likely to help you.
I would either put out a call to hire if you can not get it to work or possible post at woo or try something like http://stackoverflow.com
It really shouldn’t be that hard. Create a cpt loop on the front page of the group and then where you call the post type return the group name that matches the cpt
$cpt = some code to get the group name
$args = array( 'post_type' => $cpt, 'posts_per_page' => 10 );
$loop = new WP_Query( $args );
while ( $loop->have_posts() ) : $loop->the_post();
the_title();
echo '<div class="entry-content">';
the_content();
echo '</div>';
endwhile;
If you can not drag widgets in the WordPress admin then your install is most likely broken. This could be anything and you will need to narrow it down by deactivating everything except the very basics of WordPress. Use Twenty Twelve theme with no plugins active and then test dragging widgets, if dragging works then test each plugin one by one.
I had a gs BuddyPress site with 3,000 members and had no problem. You will not be able to run three sites on one grid. But I had to do major work on cache, minimize files and utilization of CDN
You are better off going dedicated if you think you will have more than this.
