Do I need the fog agent installed or just to register it with the fog server?
As Avaryan said, there is no need to install the client for registering. Though it can make it easier. Clients should come up as pending hosts in the FOG web interface if you have the fog-client installed on the machines. But for domain joining (and host renaming) you need to install the fog-client anyway.
My initial reaction is that you don’t have the sata driver for the P 650 G1 in your reference image.
Second reaction is what type of disk is in the 650 G1 (is it a NVMe type disk)? If so you will need to include the OS kbs that add support to NVMe disks. This is outside of what hardware drivers are needed for that model.