Does my MacBook Pro have Malware?

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

I've asked the hosts to remove the center image as it shows your personal email address. Never post such information on an open forum. Spammers and crooks love getting their mitts on live, verified info like that.

Yes, it's normal for the idmsa.apple.com page to appear if you've logged out of these forums, or shut down the browser and then launched it again. While you could still look through posts here, you would have to first log back in before you could post any new content.

Since anything with a login isn't working, it's possible the Keychain data on your Mac got mangled somehow.

To do a quick test, open the System Preferences, then click on Users & Groups. Click the lock and enter your admin password. Click the + button to make a new account. Standard is fine. Name it any ol' thing with a simple password (minimum 4 characters required).

With the new account ready, log out the main account and login to the new one. Try accessing your various sites. Though this may not prove much since it would be sharing the same keychain data. When you're done testing, you can return to the main account and delete the test account.

My guess is the keychain data is corrupt. In case that's not it, don't just delete them. Go to this folder:

/Users/your_account/Library/Keychains

Copy the Keychains folder somewhere so you have a backup.

Close all apps and open Keychain Access in the /Applications/Utilities folder.

Delete all login and Local Items. Close Keychain Access.

Now try revisiting your sites. You'll of course have to re-enter login info for many of them. But if everything now works, that pretty well proves the keychain data was hosed.

If not, you can close down all apps and return the copied keychain back to its normal location so it's back where it was without having to re-enter everything.

Old Toad's suggestion is a good one. Before playing with the keychain, do a Safe Mode startup and then followed by a normal startup. The whole issue could be corrupt cache data. A Safe Mode boot throws all of that out for the account you logged into Safe Mode with.

Boot into the Recovery volume (boot with the Command + R keys held down  - Intel Macs) or  (How to Boot an M1 Mac into Recovery Mode), select Disk Utility and run First Aid on all volumes available. Reboot normally and check.

If you have to reinstall Monterey you can do it from the Recovery volume without affecting the user data or installed 3rd party apps.

You don't have a virus. That is self-replicating malware which doesn't exist in the Mac OS.

Cookies are harmless. It doesn't matter how many you get rid of, which ones, or none at all.

Nanum Gothic, as Tom Gewecke notes here, is a Korean script font not on your system. Safari asked to install it so the page you were on would display correctly. You can download and install it for free if you want.

Refusing to let Safari download a font can't in any way have disabled it. Hold down the Shift key and launch Safari. That tells it not to attempt loading any previous pages from the last session.

Sounds like your mouse has gone bad, or needs new batteries.

Please don't tell me I have to reinstall Monterey... :o(

Okay, you don't have to reinstall Monterey. 😁

That's was part of the purpose of creating a new account. If the OS itself is damaged, you would very likely have the same issue in the test account you created. Since you didn't, then that points to the issue being in your normal account and reinstalling the OS won't change anything there.

That brings us back to possibly corrupt keychain data, or corrupt preference files. Or, possibly both. But testing the keychain data is easy, and a safe test, since you can first create a backup. It either works, or it doesn't. If not, you can copy your previous keychain folder back.

Keychain Access is in the /Applications/Utilities folder. But the path I gave was to the folder containing your personal user account keychain data.

But regardless, it turned out to be a correct guess. They keychain data had gotten botched up somehow. Good to hear things are back to normal.