For no-2, add yourself to every group and add following code in your theme’s (child theme’s if any) functions.php

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

This will allow only admins to send message to group.

For no-1: Is there any JavaScript error in your browser console?