Plugins are not updated from Dashboard > Updates

Issue 1:
Getting a lot iof these errors in server log
2018-10-19 12:03:00 Error 94.66.247.230 AH01071: Got error 'PHP message: PHP Fatal error: Uncaught Error: Call to undefined function get_header() in .../wp-includes/theme-compat/embed.php:13\nStack trace:\n#0 {main}\n thrown in .../httpdocs/wp-includes/theme-compat/embed.php on line 13\n'

Issue 2:
Can't bulk update plugin. After bulk updating plugins, a message shown that all plugins were updated suscsefully. After rechecking for updates, same plugins shown in the list again:
(22)Invalid argument: AH01075: Error dispatching request to :, referer: https://site.de/wp-admin/update-core.php