All of them MAY tolerate 5V. But they are officially 3V3 devices. Just because some schmo wrote instructions online, doesn't mean he has a clue. Lots of "it's working for me, for now" should not be reassuring. Voltage regulation is simple. LM1117 for the power, 2 resistors for the logic level shifting.
I have no idea what this means "I am operating through a development board which has a mini-USB input from my Nano. "
Firstly, what kind of ESP8266 board do you have? There are many. ESP-01 through ESP-12, NodeMCUs, Wemos, etc.
Secondly, how do you have it hooked up to your Nano?
Thirdly, why are you even using a Nano?