BuddyPress.org

I’m afraid I haven’t ever used any of the available group chat plugins for BuddyPress, but a web search shows that a number are available: https://duckduckgo.com/?q=buddypress+group+chat&t=ffab&ia=web

Here’s the bare basic code to add a page to all groups:

class my_group_page extends BP_Group_Extension {
	function __construct() {
		$args = array( 'slug' => 'page_slug', 'name' => 'Page Name', 'nav_item_position' => 12 );
		parent::init( $args );
	}
	function display( $group_id = NULL ) {
		// page code goes here
	}
}
bp_register_group_extension( 'my_group_page' );