I’m no expert with flight controllers, I’d try to test the components, connect the ESC directly to a Rx to see if it works. Connect a servos or, something you know works to the flight controller to see if it responds.
So is the Naze changing the signal, or just passing it through? Is it possible that the Arduino a different pulse width? Or not operating within the 1000 to 2000 range the Naze is expecting? Try using a PWM Rx to control the Naze, just to eliminate any of those issues.
Yes, try to control the Naze with a Rx that outputs PWM. If it works, it would suggest a problem with your Arduino, possible settings are not correct, if the Rx can’t control the Naze, it would suggest a problem with Naze. Keep in mind, I don’t know anything about Naze or Arduino, just trying suggest ways to isolate the problem.
In the videos, I didn't see you arm the board.. Are you using a switch? One thing to note is that Cleanflight/betaflight etc won't arm unless the throttle signal is below min_check (default is 1080 or something) so it will never arm with that self centering throttle stick.
Also, newer versions of BF won't arm while connected to the GUI, though I think that was added after F1 (Naze) support was dropped.