Buck converter usage
First, is related to adjusting the voltage to the desired levels. Is the output voltage dependant on the input voltage? The input voltage may vary from 12 to 18 volts or so when connected to different systems, so having to adjust for this manually is a non-starter.


No. That's why it's called a regulator because it regulates the output voltage. Regardless of the input voltage the output voltage will be the same.


  Second, assuming these are usable, what input filtering is needed for correct function? The input will be from a rectified square wave that's about 16v created from an H-bridge which is reversing polarity of the signal. Basically a 50% duty cycle square wave around a ground reference.


A full-wave bridge rectifier, ignoring the ground, as long as you then never use that ground for anything, with a large capacitor. Since it's a square wave there should actually be very little ripple.

Of course, one has to ask, what is this H-bridge square wave generator and why are you trying to power an Arduino from it?