Yes. That is correct. The raspberry pi zero is the size of a matchbox and you can power it from a good USB charger, like a mobile phone charger that provides more than 1A.
It’s extremely small footprint and extremely low power consumption. Dirt cheap too. The MicroSD card for it might cost more.
And yes, you’d have to connect it to your WiFI in order for it to resolve DNS queries using upstream DNS servers.
As for security, as long as you don’t open any ports to the public from your Nighthawk pointing to the Raspberry (port forwarding), you should be fine. No one would be able to reach it from the “outside”, it will stay contained within your LAN.
While I agree that a Raspberry Pi power source is recommended, you can get the same experience by using a 3-rd party power supply as long as it provides enough “juice”.
I personally have a good experience with non Raspberry Pi power supplies. I’m running 4 Raspberry Pi devices all powered from a non Raspberry Pi recommended power supply (granted, it’s an 8Amp USB power source) .
You do have to to use a 2A power supply (per Raspberry) if you use the GPIO for powering peripherals (sensors, LEDs etc.) or if you plan to connect a pi camera to it.
It is in the end, the users choice with what he/she uses to power the pi.
Again, if it is a low amperage power supply the pi will experience sub-par performance.
As fo the SD card, I agree.
A well established MicroSd will outperform any nameless ones that are out there.
Don’t forget another very important piece of equipment, the cord/cable. If you buy a modular power supply but use a cheap USB cable that is just aluminium foil and has a very high voltage drop then it doesn’t matter how beefy the supply is, it will never get to the SBC.