Save and Update issue

Ηι,
I am facing two problems. The first one occurs when I click "Save" after editing a user in the user management section. In this case, either the following error appears or I am simply redirected back to the main menu of the Joomla administrator without saving the changes.

Error message:
An error has occurred.  
0 Call to undefined method Joomla\Component\Finder\Administrator\Indexer\Adapter::getSubscribedEvents()

The second issue is that the CB Package Builder Search Bot and CB GroupJive Search Bot, although they appear to be updated, still show up as new updates afterward, meaning they are not actually updated.

In this case, either the following error appears or I am simply redirected back to the main menu of the Joomla administrator without saving the changes.

Are you using the new CB Search Bot plugin to allow Joomla's smart search to index users? You can find it in System > Manage > Plugins as "Smart Search - Users". If so what Joomla version are you using?

The second issue is that the CB Package Builder Search Bot and CB GroupJive Search Bot, although they appear to be updated, still show up as new updates afterward, meaning they are not actually updated.

The old search plugins won't be uninstalled for you as to prevent legacy search components from losing functionality. So you'll need to go to System > Manage > Extensions and remove the old "search" type plugins if you no longer will be using them.