Radek,
I can tell you that I'm not having any trouble with the new icons in Backup, I'm using Firefox as well. It is possible we have a bad upgrade and some files are missing. Please download Akeeba Backup from our Downloads page and install it twice, back to back, without doing anything else in between. Do not uninstall, that will cause you to lose all your settings and possibly your stored backup archives. This install twice trick usually works around a bug in the Joomla! installer where it forgets to copy all of the files in an install or upgrade.
We don't officially have support hours over the weekend, but it makes Monday easier...
Dale L. Brackin
Support Specialist
English: native
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!
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My time zone is
EST (UTC -5) (click here to see my current time in Philadelphia, PA)