Hey there CornWallis1,
Thanks for reaching out to the Apple Support Communities.
To get started, what happens when you attempt to open the App Store app on your Mac? For example, do you see any alerts or errors, or does the App Store window just appear as a blank white window? For steps that can help with troubleshooting issues with apps not opening as expected, check out this link here: If an app on your Mac stops responding, closes unexpectedly, or won’t open - Apple Support
1. Quit and reopen the app
Quit the app, then open it again. If the app won't quit, force the app to quit. Then check to see if the problem with the app is fixed.
2. Restart your Mac
Restart your Mac. Then check to see if the problem with the app is fixed.
3. Check for updates
To see if updates are available for the app, open the App Store, then click Updates. If updates aren't available for the app, update the software on your Mac. Or if you didn't get the app from the App Store, look for updates to the app on the app developer's website. Then check to see if the problem with the app is fixed.
4. Reinstall the app
Delete the app. When you do this, you might lose data that was stored in the app. Then redownload the app. If you didn't get the app from the App Store, redownload the app on the app developer's website. Then check to see if the problem with the app is fixed.
As for the other issues you mentioned while a restart may help, if you do continue to have issues we would recommend testing the issue in safe mode to isolate the issue further. Safe mode can help you to determine whether an issue is caused by software that loads as your Mac starts up.
For steps on how to boot into safe mode, and what to do if the issue does or doesn't occur in safe mode, check out this next link here: How to use safe mode on your Mac - Apple Support
Intel processor
1. Turn on or restart your Mac, then immediately press and hold the Shift key as your Mac starts up.
2. Release the key when you see the login window, then log in to your Mac.
3. You might be asked to log in again. On either the first or second login window, you should see ”Safe Boot” in the upper-right corner of the window.
Keep us updated on the results after going through the steps in the resources above, and we'll continue from there.
Have a great day!