Why doesn't the phone have a camera app?

When is the last time you rebooted (restart)? If you always simply put your phone to sleep, it's probably worthwhile rebooting from time to time. I would try that first. If you're not familiar with the reboot process, with the phone on, press and hold the power button (top button, right hand side while facing the screen). One of the options that will pop up is "reboot". Select that and the phone will restart.

I don't know if it's possible to uninstall, then reinstall the factory camera application with this phone, but that would be the next possibility I'd try if the reboot doesn't help. You might also be able to install a 3rd party camera app but if the stock app can't communicate with the camera, there's a good chance any other app would also fail in that regard.