Can we deauthorize a plugin before a clean install of Windows and reauthorize later again for avoiding the license system takes the new installation as a new computer?.

No worries, under normal use (and bare in mind you are allowed to install on any number of computers that you own) you will not hit a limit. We count and show the number of installations for you to detect if your registration has been stolen and for our system to monitor excessive installations that could be in violation of the license terms.

So just to confirm, we don't need to deauthorize a previous installation at all. I recently had a death in my computer family and had to reinstall on my new machine. There is likely no way I will ever be able to uninstall my previous installation.

Correct, you don't need to do anything.