You answers to item 2 and 3 seem a bit contradictory.
Starting with item 2. Can you confirm this is what happens. While unit is on and with nothing connected to the clamp you press the override for 3 seconds - this will cause the two output relays to engage with an audible click. At this point measure the voltage at the clamps and it should be 12.3 or so.
Your response to item 3 confuses me because you mention that in override mode the voltage is 1.6V but in item 2 you say it "works" which would mean the voltages at the clamps are 12.3 like I stated in item 2 test. It would be helpful to know if the override is working correctly.
When the override is engaged all battery power transferred directly to the clamps via the two relays. When not in override there is close to no voltage at the clamps. It's that simple.
If you could clarify this confusion that would be helpful.
As for further testing measure the resistance between R305 on the side closest to the number 5 and the main battery ground above R106.
Take this resistance measurement with all JST plugs disconnected and then with just the relay plug connected.
Remember the battery balance plug and the relay plug are the same. Don't mix those two up
Jerry