Ok, we found out what was the problem.
Installed Prestashop directly from Plesk 12, using its application installer.
And the thing is Plesk using some kind of modified installer .zip of Prestashop, full with bugs.
Why is it true? Because after that installed Prestashop from original .zip from prestashop.com, uploaded via FTP, and after that everything worked well, without any errors and bugs.
CDN is worked fine,too.