Is this a scam/Is my computer unsafe?

That’s a tech support scam popup. 

Fake Tech Support Scams – see video from the MS Digital Crimes Unit https://www.youtube.com/watch?v=hQpm2ldzUno

You handled the potential issue quite well.

Usually you can close down the browser without issue though sometimes you need to close it using Task Manager (Ctl, Alt, Del). Occasionally you may need to do a hard shutdown using the Power button.  When you restart the computer do not restore your browser if asked to do so.

Any new browser extensions or items in startup that need to be disabled/removed?

Some users report that programs such as ublock Origin or another ad blocker will help prevent these popups from appearing.

For further information see Beware of Phony Tech Support Scams

And

https://www.microsoft.com/en-us/wdsi/threats/support-scams

If the issue recurs you may want to follow the steps in https://malwaretips.com/blogs/remove-tech-support-scam-popups/ You may not need to use Hitman Pro (available if needed as a 30 day trial) but you may need to reset your browsers.

Regards...

http://blog.emsisoft.com/2015/01/27/top-10-ways-pups-sneak-onto-your-computer-and-how-to-avoid-them/

My wife was using her computer at work when the following image popped up on the screen.  She had to go to task manager, to get rid of them.  Is this a legitimate error message, or is the computer now insecure.   Do we have to worry about someone monitoring what we are doing with the computer, i.e. tracking our key strikes? 

Any one know what to do next.  We have the full security suite that came with windows 10 running on the machine, shouldn't this have caught something?

Agreed, that's a scam.

This is the checklist I use to determine if it's a scam:

Is it in a web browser? (Browsers are not anti-viruses.)

Is the grammar poor? (Banks almost always are professional enough to use spellcheck.)

Does it make sense? (CRITICAL_PROCESS_DIED does not mean that someone is trying to steal your bank account info. It actually means a critical process died and Windows needs to reboot. Also, you would not get that in a browser window.)

Did an antivirus scan turn up positive? (I once got hit with one of those scams. My CPU went up to 100%-another dead giveaway- and I had to kill Chrome manually. I ran an anitivirus scan and, as it turns out, I had a hacking tool on my system, according to Norton. Wonder where that came from ;). )

If you said yes to all of these questions-or even a few-, click away from it, run a scan, and believe that your bank account is fine and that you do not have a virus on your computer.

Best regards,

Michael.