Hi,
1 - To remove this warning, you can replace the line 242 of the plugin by
if($group && !empty($product->order_product_option_parent_id)) continue;
2 - The debug mode will store some data in the payment log only for the IPN part (server-to-server notifications from Authorize)
3 - Ok
4 - Regarding the PHP warning, the order is confirmed, so you should have the "end" page with the Authorize.net data.
Now depending your mode (DPM, AIM, etc), you might have a form which will be submitted or an iframe.
So having more details about your configuration and what exactly you're doing will be more than helpful.
Regards,