Actually, that's three questions:
"what are the 3 pin connectors for on the top of the gimbal"
Those are for connecting to the "Hot Shoe" arrangement of the Q5004K. They are the same three functions as the three wire cable normally used to connect a CGo3 to a Chroma.
"can they connect to the base of the chroma?"
Depends on how bad you want it. The mount for a Q500 4K will not work because of the screw spacing. But I think the mount for a Typhoon H will fit with employment of some spacers or maybe shell modification. There is not much room inside the battery compartment for the wiring. I started to install the "hot shoe" system on mine a while back and decided the benefit was not worth what it would take to route the wires inside. You might have enough clearance between the mount and the shell to route the wires externally to the existing plug on the Chroma shell. At least it would make the camera faster to mount and dismount.
"should the gimbal cables be visible externally as in this photo?"
Yes. That is normal.