• Firefox has an export to html option for exporting bookmarks (to a .html file, named some_name_you_gave.html)
• Firefox has a Bookmark backup option for backing-up bookmarks (to a .json file, named similar to bookmarks-2011-07-27.json but with the date of the backup)

Where did you get the file backup.file. That is not a file name/extension that will be recognized by Firefox. If you used Bookmarks > Show All Bookmarks > Import and Backup > Backup, it should be a .json file and would be dated similar to the one in the second bullet above and would be in your profile folder, in a folder named bookmarkbackups

• How to find your profile
• How do I import, export or back-up bookmarks

In Firefox Backup option, I think. I made it quickly and saved it on desktop, put on HDD. Didn't looked at extension, but it was name Firefock Backup.file The text inside it is formated like: '{"title":"","id":1,"dateAdded":1219838271095689,"lastModified":1270308249669000,"type":"text/x-moz-place-container","root":"placesRoot","children":' and so on. Is there any Importer compatible with this kind of... backuping?

How can a browser export unrecognisable file I do not know. It was on the old version, 3.6 or something.

That is JSON bookmarks code. That type of file needs to be restored, not imported.

Windows is good for hiding file extensions that it thinks it knows, which makes it difficult for users to know what the file type is. As far as Firefox goes, Mozilla relies on the user to be sharp enough to import what they exported, and to restore what they backed up. Each type has a separator between them in Library > Import & Backup.

In WinXP there's an option for that in the control panel > folders options -> view - hide extensions for known file types = un-check it
Sorry, I haven't used Win7 so I don't know the exact names for everything relative to that pref.

I have already tried that. Yes I have tried restoring it. It didn't worked, I have tried changing into .JSON and it said 'Unsupported file type'.

Tried renaming the Firefox Bookmarks 'bookmarks-2011-07-23.JSON' and it still didn't worked.