I have successfully translated parts of my test site into Danish using the exported language from the Translation Centre. Here is what I did.
First of all you were missing the .mo, you need to go to the Translation Center and export the file as a .po which you already have and as a .mo. I called the files the following:
I then uploaded these files to /wp-content/plugins/pagelines-customise/language/
Then I opened the wp-config.php file and where:
I changed to this:
I then cleared by browsers cache, and parts of the site were translated (see image below and the search filed label) which is no longer "Search" but "Søg".
Also, on your PL Debug mode info, you have the following:
PHP Open basedir restriction : Yes! <=== This can cause PHP to refude to open certain files.
PHP Magic Quotes gpc : Yes (bad) <=== This has been completely removed as of PHP version 5.4
I recommend you contact your host and ask them to resolve the open_basefir and to upgrade your PHP, so magic quotes is removed.