I have a subscription, but it says I do not have a valid subscription

You need to enter the Download Key in the settings of Regular Labs Extension Manager.

You can find the settings by clicking on the Settings button in the Regular Labs Extension Manager component.

You can find your download key in your Downloads overview (after logging in).

I get the message: "Could not retrieve data from the Regular Labs website. Please try again later"

The reason can simply be because you are no longer logged in. In other words, your session has expired.
Try to reload the page and log in to the administrator again.

Another reason could be that your server is blocking the regularlabs.com domain name or IP address. Or is blocking remote url calls alltogether. Ask your host if they can see why the page is failing.