Are you sure you can use that diagram?Most A/Ds must have BOTH inputs voltages within their own VCC-GND.Or even less than that (common mode range).I don't see any reference to the A/D's ground (or VCC).
The op may find this info to be useful https://www.arduino.cc/en/Tutorial/ReadAnalogVoltage, which was found by entering the words "arduino uno read volts" into my favorite internet search engine.
Also, this may be useful http://www.ohmslawcalculator.com/voltage-divider-calculator
Yes, I am sure. I'm using an ADS1115 which has its upper and lower limits at VCC+0.3V and GND-0.3V.
Also sure, can't do that if you don't refer the inputs to some voltage.Imagine the bottom part of the 1k resistor 'floating' on about -0.5volt.Then the top part of the resistor is about -0.25volt.Both inputs are outside the measuring range (GND-VCC), and the A/D will return zero.As said, both inputs MUST be kept within VCC/GND of the A/D.
As far as I understand it, the ADC references differential, meaning A0 against A1 (and not against GND).
Please explain the real purpose of this circuit. "crude input protection" does not make sense.
No, that is not how the ADS1115 works. The inputs are referenced to the ADC ground and internal VREF, and the difference between them is constructed.
I don't see any problem in measuring a floating voltage that does not share common ground with the system containing the ADS1115.