The first error message was, as you figured out, a problem with the PHP opcode cache "remembering" the old version of our code which is no longer installed.
The second problem you have is very likely also related to the same issue. The method you are reporting as missing is actually present in the /media/fef/fef.php file on your site. It's part of FEF 2.0 which is shipped with Akeeba Backup 8.0.0.
Please open that file with a text editor and look for the line
public static function loadCSSFramework(bool $withReset = true, bool $dark = false)
It should be line 80.
If the line exists you need to ask your server technician to reset your PHP opcode cache.
If the lines does not exist it means that Joomla dropped the ball while updating your site. It happens to approximately 0.3% of sites. With several thousand sites using our software we get to see it quite a lot every time we make a new release. There is a manual workaround.
Download the ZIP file for Akeeba Backup for our site. Extract it. There is a file called file_fef.zip. Extract it. Upload all of the extracted contents into your site's media/fef directory.
You may have to reset your opcode cache again after doing that.
Nicholas K. Dionysopoulos
Lead Developer and Director
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