It’s possible that your IP address has been flagged for excessive bandwidth usage and has been blocked from accessing the demo website. Let me know your IP address and I’ll check that for you → http://www.whatismyip.com/
I’ve never seen errors like that before. Normally if the WordPress Importer plugin comes across a post type that it doesn’t know about then it displays the name of that post type in the error message. For example…
Failed to import “Lorem Ipsum Dolor”: Invalid post type portfolio
Or…
Failed to import “Footer - Top”: Invalid post type static_block
So what I did was I searched the internet for “Failed to import post tag” and here is what I found → http://wordpress.org/support/topic/failure-to-import-and-invalid-post-type-errors
It seems that this issue may be related to your server settings and is not related to the theme you happen to be using. That thread in the WordPress support forum includes a workaround you can try. If that workaround doesn’t work for you then I’d recommend starting your own thread in the WordPress support forum to see if anyone has any other ideas.
But first let me know your IP address so I can check if it is being blocked.