PeterD answered most of your questions, but I'll see if I can add a little insight!
The "click" you are hearing near the day tank is the solenoid in line between the fuel pumps and the day tank. It is controlled by a float switch inside the day tank. Based on your description, its operation is normal.
I have purchased a few sets with multiple independent problems like this. I spent just a few minutes looking at the schematics...no single fault popped out at me that could cause all of your symptoms. Your starter and fuel pump issues may be connected, but I think the coolant gauge is a separate issue. I find it helps to focus on one single symptom. Many times, when I find the problem with that one symptom, it sheds some light on the other symptoms.
Let's start with the fuel issue...its an easy one to troubleshoot. With the master switch in run and the battleshort switch in battleshort, your fuel pumps should be clicking. Since they aren't, lets start there first. Pull the plug for the power wire to one of the pumps and, with the master switch in run and BS switch in BS, check for 24v between that wire and ground. If 24v is present, the pumps need to be cleaned (I often find both pumps seized up with paint chips, sand, rust, and other nastiness). If 24v is not present, work your way back to the master switch. Power for the pumps passes from the control cubicle, through a cable harness and a couple of plugs, through the special relay assembly, and out to the pumps. I would probably start by checking for power at TB1-8 in the control cubicle, as it is easy to get to without taking anything apart. No power there, work your way back through the master switch. Power there, then work your way through the special relay box toward the fuel pumps.
Use the schematic on Page 345 on TM-9-6115-464-12
Once we get your fuel pumps working, we'll focus on the other symptoms if they all still exist.