I got my Fairphone 2 a few weeks ago and have similar experiences.
As for the cameras, my back camera works but front-facing does not with the included software with Fairphone Open 17.11.2. I installed another camera application from F-droid and both cameras work!
As for random reboots - I get on average maybe one a day. Trying to narrow down where they come from before searching for help but so far to no anvil - no apparent pattern in my case!
You have a new camera module but run an old operating system. → Update your OS or check the updater app to see which OS version you are running and compare it to the oslist.
Your camera module is not connected well. → disassemble the camera module and clean the connectors before putting it back again.
Your camera module is not working. → Only support can help you.
Please continue here and check the first post there to get some tips.
If they don’t answer in the next days give them a call and have your ticket number ready as well as your IMEI and order number if you didn’t yet include them in the support ticket.
PS: Since the camera issue seems solved now I’m setting this topic to auto-close in a few days. For the random reboots please continue in the topic I linked above to avoid duplicate threads.