BuddyPress.org

Displaying groups on any page is relatively easy – use one of the widgets. If your target page doesn’t have a widget area where you want one, you’ll have to update the template file (in your child theme) and add a widget area. Register the new widget area through your functions.php file. There are a fair number of resources on the ‘net for how to create new widget areas.

Displaying some forums posts from each group at the same time is going to be much more complex. It’s not going to be easy unless writing a fair bit of code is something you find easy. It can be done though.