The camera flash on my Samsung Galaxy Camera isn't working; despite deploying the flash using the switch on the side, and...

Your camera's screen sounds like it could be damaged. To replace it, you'll need to disassemble the camera by removing the screws holding the case together, and use a plastic prying tool to pull the case apart. Another potential problem is that the motherboard may be faulty; this would also require you to take the camera apart, this time to replace the motherboard. You can find detailed guides on how to do both of these on the camera's Troubleshooting Guide.