It sounds like something is seriously messed up with class autoloading
or maybe some of your MediaWiki files are missing.
LocalisationUpdate\\Reader is part of the LocalisationUpdate
extension. ApiBase (includes/api/ApiBase.php) is part of MediaWiki
I would suggest re-installing MediaWiki (in a fresh directory) and
seeing if that fixes it (If you need to keep the data in your current
install, be sure to copy over the LocalSettings.php file, the images
subdirectory and maybe the extensions subdirectory).
Also, I would note that MediaWiki 1.27.0 is rather outdated and has
publically known security issues. 1.27.4 is the latest release of the