These (appalling designed) modules are controlled by a PNP transistor connected to 5V.
They can only be controlled by 5V - which requires an external transistor (which kind of negates the point of a module because you could just control the relay directly).
See Can you use a 5V Relay Module with the Pi?
Some claim they can be used with 3.3V - but the relay ...
This behavior is, in fact, a bit unusual, since most devices would recognize 3.3V as high, even if the power supply is at 5V. But it seems this is not the case here. That's not a big problem, though. If it works at 3.3V and the relais is (as I expect) properly separating the control side from the switch side you're all set.
If I understand your objectives correctly, it seems that your idea is generally sound. But, the devil is in the details as they say.
Reviewing your diagram:
It appears that the purpose of the Low Battery Cutoff Switch and the N.O. 12 V Relay is to signal the RPi (via GPIO input) that it should execute a shutdown soon. However, 12.3V seems too high for a low-...
No. The GPIO are set to default values at power-down by the hardware. Those are the values that are set when the power is restored.
At power-up all GPIO are set as inputs. GPIO 0-8 have weak internal pull-ups enabled. The other GPIO have weak internal pull-downs enabled.
These settings may be overridden by software during boot.
If you want to defeat the ...
As a general rule, bidirectional GPIO pins will default to being inputs when the chip is reset or power is first applied.
It would help if you included a schematic for your connections to the relays, but if you want the pins to default to a low voltage then you probably need to add pulldown resistors to those pins.
you need something like a dead man switch. I cannot draw schematic, but i would use two relay system. One relay as you said that can pull pin low to shutdown, another (3.3V) that connects power to Rpi throuth COM-NO contact. You need to bypass this COM-NO with pushbutton. As soon as RPi boots, put a script that will turn on 3.3V Relay with some GPIO, after ...