Greetings, KristofferO.
Congratulations on your new iPhone X! I see that you're experiencing an issue with the rear camera, however. It will only take pictures in Portrait mode. Any other results in a white/blank screen and the pictures come out the same. I can understand your disappointment and I'm happy to help.
How to back up your iPhone, iPad, and iPod touch -- Since restarting and forced-restarting your phone didn't resolve the issue, please be sure to have a fresh backup to keep your personal information safe. In order to back up your Health data, the backup needs to be encrypted. iCloud does this automatically, but iTunes doesn't. If you'd like to use iTunes to back up your phone, refer to this article: About encrypted backups in iTunes
If you can't update or restore your iPhone, iPad, or iPod touch -- Even though the title of the article isn't specific to your issue, the section titled "Put your device in recovery mode and set it up again" will walk you through all the steps to reinstall the iOS software on your device. Test the issue once your phone has returned to the Home screen.
Let me know how that goes.
Take care!
