Add following code in your theme’s (child theme’s if you are using) functions.php

add_filter( 'fep_get_option', function( $value, $option ) {
	if ( in_array( $option, ['can-send-to-group', 'allow_attachment'] ) ) {
		if( fep_is_user_admin() ) {
			return true;
		} else {
			return false;
		}
	}
	return $value;
}, 10, 2 );

This will allow to send group message and attachments only by admins.

May you explain “the user could only add himself to a specific group” a little more? Suppose you have 5 groups but you want your users can add themselves only specific 2 groups?