Ok, both issues might even be related.
As for fixing, I would start with fixing the update process, since everything else can be fixed from there onwards. Unfortunately, windows being stuck op updating can have quite some causes. I always use the [https://blog.krissmilne.tech/windows/windows-7/windows-7-stuck-on-checking-for-updates|following guide] to help me through the steps. Even the most stubborn stuck updaters have managed to start working again using these, though you'll need quite some patience to try them.
If you're the more inpatient kind of user, start with step 4. In my experience this fixes about 90-95% of the updating problems. Rebuilding the update base afterwards will take quite some time though, depending on how many updates are already installed on the system.