Hi @Jetson-Nano
Happy to continue helping.
Regarding your updated design first:
"I2C Bus Configuration: Regarding the I2C bus, should the I2C lines be connected in parallel to both the Lepton Module and the I2C GPIO expander?"
-- Yes.
"Lepton Reset/Power Down Pins: Concerning the Lepton Module's RESET_N and POWER_DOWN_N pins, should the existing resistor-capacitor (RC) network connected to the RESET_N pin be retained, or can it be omitted?"
-- We do not have any RC delay on the reset line since it is all GPIO controlled.
"I2C GPIO Expander INT Pin: For the I2C GPIO expander, is it permissible to leave the INT (Interrupt) pin unconnected, or does it require termination?"
-- It is an output and we do not use it, so N.C. is fine
I2C GPIO Expander Software Configuration: From a software perspective, is the I2C GPIO expander a plug-and-play component, or does it require specific configuration?
-- It is supported at that HW address by default with voxl-lepton-server (I think that it what is called, Alex can correct me if I'm mistaken)
However, your updated SCH has a couple errors:
-
Your LDO input and output caps are not correctly done. They are in series, not shunts to GND as required:
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The Pull-down R on the GPIO expander is not correct. The ADDR pin will always be HIGH due to the direct connection to 2.8V, but our default is LOW (see the snippet from above): 
-
Also, the GPIO expander is meant to drive the RESET input of the Lepton, not the PWR_DWN input: 
Now, as to your existing board not powering on, I have a clue for you...
Our very first lepton board we failed to notice the pin 1 hole in the Molex socket, and that is important since it sets a keying for the Lepton module. If the module is inserted incorrectly (90 or 180 off) it will clearly not power up. Pay close attention to the hole in the socket for pin 1 and two vs one slots in the socket which set the orientation.


Keep us posted and hope this helped.