2012 MacBook Pro practically unresponsive after unplugging external monitor

Oh my goodness! You have some work to do. :)

Major Issues:
  Anything that appears on this list needs immediate attention. 
  No uptime - No system uptime found.
  No operating system found - Unable to determine operating system version.
  Poor performance - EtreCheck report shows poor performance. This is unusual.
  More than one antivirus app - This machine has multiple antivirus apps installed.

Start with the Major Issues:

I see EtreCheck could not ID your OS. I think that's a little strange... obviously it's running something. Possible could not be determined because of software conflict.

Get the the antivirus apps Avast and CleanMyMac shut down and removed from the machine. Discontinue them altogether until this gets sorted out, and then keep them the heck away from the machine. More on that later. Suffice it to say that multiple antivirus/antimalware apps tend to not play nice on the same machine. And CleanMyMac is commonly looked down upon in the community as "less than helpful". Turn them off and uninstall them as per the publishers' instructions if you can.

Remove CleanMyMac from the User Login Items (navigate: System Preferences > Users & Groups > Login Items then select it on the list and click the - (minus) button.

When that is done you could try a reboot... but not so fast. If you have left Etrecheck open, you have an opportunity to let it help you review and resolve the list of unsigned files it has identified in Minor Issues.

Minor Issues:
  These issues do not need immediate attention but they may indicate future problems or opportunities for improvement. 
  High battery cycle count - Your battery may be losing capacity.
  Unsigned files - There are unsigned software files installed. They appear to be legitimate but should be reviewed.
  System modifications - There are a large number of system modifications running in the background.
  32-bit Apps - This machine has 32-bits apps will not work on macOS 10.15 “Catalina”.
  Limited drive access - More information may be available with Full Drive Access.

Delete any unsigned files that include "Avast". I count six, located in /LaunchAgents/, /LaunchDaemons/ and /Application Support/. Don't forget to empty the trash.

With the antivirus and anti-malwarejunk out of the way I think you can try a reboot now and see what happens.

We can address the other items on the lists after, but let's see how it goes with these tasks done.

Hello.

Sorry to hear you’re having this problem with your Mac.

It looks like you've done quite a bit of troubleshooting on your own and in the right direction.

I think we can help you, but we’ll need a little bit more information about the computer

EtreCheck is an awesome little app that displays important diagnostic and debugging information about your Macintosh and allows you to copy that information to the Clipboard. It is very highly regarded and meant to be used with Apple Support Communities to help others help you with your Mac.

Please navigate to the Mac App Store and download the free version of EtreCheck OR please click EtreCheck.com where you will also find the app. Once you’ve downloaded the app and created the report please post it with your reply to this message. 

For instructions on how to download your EtreCheck report and attach it to your reply to this message, please click  How to use Add Text when posting…

We can then use the EtreCheck report to look for obvious issues that may be causing your problem and advise how to correct them.

d.i.

edit- it's obvious from the description of your issue that this suggestion may be difficult to get done. But it would definitely be helpful to understand what's going on.

How does the Mac run in Safe mode

http://support.apple.com/kb/ht1564

This will not load any 3rd party additions, it will load some more conservative Apple drivers (may cause screen flicker), and it will clear some kernel caches (a cache is saved data in a form that can speed up a program, but is totally redundant to the original source, and thus can be safely cleared).  Booting into Safe mode is just an experiment, but can frequently eliminate any 3rd party interference, or a cached item out-of-sync with the world.  (Verify Safe mode via Applications -> Utilities -> System Information -> Software -> Boot Mode -> Safe vs Normal)

  Antivirus software: Apple, Avast,  and CleanMyMac

Dump Avast and CleanMyMac

  disk0 - Samsung SSD 860 EVO 500GB 500.11 GB (Solid State - TRIM: No) 

Suggest enabling TRIM

http://osxdaily.com/2015/10/29/use-trimforce-trim-ssd-mac-os-x/

Applications -> Utilities -> Console

This should show you the behind the scenes messages being logged (something only a developer could love). Your goal is to see what it looks like when things are normal, and then watch what happens why you remove the display. Is there a sudden uptick on activity?

I do not know if it will help identify anything or not, but it it goes wild, it might. If it doesn't seem to change much, then it was a failed experiment.

And it would be very interesting to see how the system behaves when booted into Safe mode as requested.

Well, that's a positive step in my book.

BobHarris posted a solid suggestion above re: rebooting into safe mode. I suggest you try that, and while in the mode run the Disk Utility > First Aid against your SSD and let's see what it can tell us.

Please, please, please do a backup of your machine before proceeding here, assuming you haven't been able to very recently.

edit - baby steps.

Very good. We await your return.

By the way and FYI, booting into safe mode can take time. It's not uncommon to wait ten minutes or more, so be patient.

1.75 hours! Yikes!

EtreCheck can usually get the job done in just a few minutes... 3-6, give or take.

I'd suggest that your MBP is experiencing a drive failure or data corruption on the ssd. That would seem very coincidental to the act of unplugging the mini display/hdmi cable, but I suppose it's not outside the realm of possibility.

If you have the resources, I would suggest you create and try to boot from a bootable external drive and see how that goes.

If you can make that happen and the machine responds appropriately, then it would point the finger at the ssd and facilitate making making corrections to the internal drive, either repair or replacement.

I hope you have been using Time Machine or some other data backup system.

edit - If you have another contemporary Mac, you might also try to access the MBP and do diagnostics by booting the laptop in target disk mode.