"Activating the icon from the Dock does nothing."
Clicking on an app icon in the Dock will make that app active. If that app is Finder, then clicking the Dock icon will open a new Finder window if there is not one currently open. If you have a Finder window open in another Space and the option, "When switching to an application, switch to a Space with open windows for the application," is enabled, then you'll be taken to that Space.

More info:
Use the Dock on Mac - Apple Support
View open windows and spaces in Mission Control on Mac - Apple Support
None of the menu shortcuts work.
Your screenshot shows exactly what mine shows, and nothing is 'not working' about Finder for me.

What happens when you select an item and click it? If nothing happens, relaunch Finder. Hold down the option and control keys and click on the Finder icon in the Dock, then select Relaunch.

If you mean the keyboard shortcuts for the menu items don't work, and if by 'highlight-click' you mean control click, then check your keyboard mappings for modifier keys in System Settings > Keyboard > Keyboard Shortcuts (button) > Modifier Keys. Click Restore Defaults to remove any unexpected mappings.

More info: Change the behaviour of the modifier keys on Mac – Apple Support
From my perspective, your post is rather vague (are menu shortcuts menu items or keyboard shortcuts, 'highlight-click' is not a common term, etc.), so the following are more general troubleshooting steps:
Have you rebooted your Mac? If not, that's the first step. If that does not help, then see if the problem is present when you boot in safe mode. That process performs some system cleanup and clears caches, and also disables 3rd party extensions that may cause problems.
Start up your Mac in safe mode - Apple Support
If that does not correct the issue, test in a new user account. A newly-created user account will have all settings at default, and if the issue does not occur in that new account then it provides guidance on what may need to be changed to correct the issue.
Add a user or group on Mac - Apple Support
Once the testing is complete, the new account can easily be deleted.
Delete a user or group on Mac – Apple Support
Those steps will help to isolate the problem.