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Your cache is rather outdated, please ensure your background tasks are running. Once I cleared all php files in your /datastore directory, recovery mode worked. Please try now and do not enable any third party add-ons which are not compatible with the release you're on or PHP version.

Your site appears to be working correctly at the moment. Are you still seeing issues?

Thank you, I am investigating now. Please do not login to the admin panel or make any changes to the install.
I'll update this topic when done.

You have a third-party plugin called "Pages Category URL" but you do not have Pages. Therefore, it looks like it is trying to access things which you do not have thus an error is appropriate. You will want to uninstall it.

If you're using any third party add-ons, I would suggest disabling all and trying again.
If not, we would require access:
We would need to look further into this for you, however the access details on file appear to be incorrect or missing. Could you please update these details by visiting your client area, selecting the relevant purchase, then clicking "Review/Update Access Information" under the "Stored Access Information" section. 
We look forward to further assisting you. 

It is pretty outdated. It is currently in version 1.3.9.

One of your 3rd party applications or plugins isn’t compatible with the current release. 

You probably have an outdated (now due to the new IPS version) plugin/app. Disable all 3rd-party resources and test it again then you’ll have to enable one by one to find the one causing the issue. 
Or you can try to guess by its name. See if some of them mentions registration, etc.