David,
Yes– the application ID is required for LIVE transactions.
For error_logs, you will want to go to a folder in your files that is just titled: error_logs (sometimes just yoursite/public_html/error_logs with cPanel)
If you have trouble after setting your application ID (or if you need your application ID) please get in touch with paypal so they can assist you and tell you what they can see from their end.