Ok, you have definitely a "problem".
1st - Let's check if COPS works with your iOS apps.
-> startup Marvin and add the "COPS-demo" library to your OPDS Catalogs
-> see pictures 1 + 2 attached
If this works and you can connect to COPS demo and download an read "Alice's Adventures in Wonderland" then
2nd - check the COPS installation on our Synology.
-> open Config_local.php
-> check if the following line is present
$config['calibre_directory'] = './calibre/';
Where calibre is the directory your ebooks are in. You may have named it different like "Calibre library"
3rd - Connect with Marvin to your Synology from within your Lan.
What output do you get? ........... (to be continued?)