From the official CalyxOS documentation:
The device automatically checks for, downloads and install updates.
A reboot is required to finish updating, you will get a notification for that.
I think that is what happend.
VPN not working and not being able to install Apps to me sounds like something that can happen when you are in the middle of an update.
I think you should just reboot your phone.
If you feel, you need more information, it would probably be best to get in touch with CalyxOS community.