David E. Ross wrote:

I have Windows 7 Ultimate SP1 x64.
However, I cannot install updates to two applications ...
Both throw up error popups claiming my Windows version is not compatible.
These a
* Thunderbird 60.0 (update from 52.9.1)
* Skype 8.27.0.85 (update from 7.36.0.150)

I've used Thunderbird on Windows 7 Home x64 (but went back to MS
Outlook). I've never bothered to install Skype and even reject (hide)
the Windows Updates for Skype (I don't need updates for a product that
is not installed). I'll only address the Thunderbird update issue.

Thunderbird automatically checks for updates every day. If you disable
auto-updating and prefer manual updating, use the menu - Help - About
Thunderbird. Mozilla has never understand the difference between
checking for updates and applying updates. To Mozilla, checking for an
update means also downloading a new one, if available, and immediately
applying it. Very rude. That has Thunderbird go to Mozilla's file
server to get the correct file to download (and run).

Are you using Thunderbird to check for a new update (and then apply it)?
Are you using a web browser to go to the Thunderbird download page
(https://www.thunderbird.net/en-US/thunderbird/all/), picking a file for
the full installer, downloading it, and running it yourself? If the
latter, are you sure you are picking the Windows download and not one
for some other OS, like macOS or Linux?

As I recall, you cannot install programs in Windows' safe mode (that use
MSI to install themselves). You could use msconfig.exe to disable most
(but not all) startup programs, reboot into Windows' normal mode (but
without loading all the startup programs), and see if the installer then
works okay. If the installer works under a neutered Windows, something
you load on Windows startup or on login is interferring with the
installers.

Are you running the installer with admin privileges?

Did you disable the Application Experience service (AeLookupSvc) in
Windows that lookups up processes to determine the compatibility mode
under which to run a program?

Before you run the installer, did you check in Task Manager's Processes
tab that there were no instances of thunderbird.exe still loaded?

Mozilla started adding SHA-256 signing certificates to Thunderbird back
around version 38.5.1 during Jan 2016. I believe this was due to new
signing requirements in Windows. Some users encountered invalid certs
and had to revert back to a prior version with a valid cert (and then
use auto-update or update check within Thunderbird).