You can safely use the Health Check and Troubleshooting plugin on your main site without any staging site. Once you enter troubleshooting mode, all other plugins will be deactivated and you’ll be switched to a default Twenty* theme. This will only affect your view, other visitors will see your normal site.
In troubleshooting mode, you should be able to do everything without error. If not, your WP installation may have become corrupted. In such a case you should perform a manual update, even it’s to the same version. The point is to refresh all files from a fresh download.
If troubleshooting mode resolves your problems, then they were due to a theme or plugin conflict. Via the Troubleshooting admin bar item, restore your normal theme and plugins, one at a time, testing after each. When the problems recur, the last activated module was the cause.
If WooCommerce is already deactivated on your site, it wouldn’t be the cause of your problems. But if your site requires it to be fully functional, activate it like you would any plugin from the Plugins admin screen. But I suggest waiting until you resolve your current issues before activating it.