iMac gets stuck while checking for updates

Adobe has not been supported in Flash format for over a year.

Visit this website to remove it.

https://helpx.adobe.com/flash-player/kb/uninstall-flash-player-mac-os.html

As for the other software updates not working:

1. Backup your data.
2. Determine if the update you are going to is compatible with both your hardware, and software.
3. If you are running Big Sur, and want to get to Monterey, follow the requirements on this page.

In Systems Information > Software > Installations, the list is displayed in alpabetical order, so a lot of adobe installs may show first.

You can rearrange the list by clicking two times on the top of the "installation date" column, then it displays the last installation first.

The list is build from a file in /Library/receipts/InstallHistory.plist. You can look there to see if it is not corrupted.

I doubt that it will solve your problem with checking for updates getting stuck.

My guess is that you cannot get trough to the server because of internet connection problems.

The update that is shown, is probably the Monterey update. Since yesterday I got an entry in the installations list "MacOS Installation Notification version 2" and now i also get a 1 Software update notification for Monterey by the way.