Can the ADS1118 ADC converter accurately read a voltage close to GND?
Looking in the datasheet I see:



note that these are not the maximum ratings but the recommended operating conditions!

Which is good, basically TI says: please use it under these conditions.

So we can use the inputs in the whole supply range.

So your SITUATION ONE and SITUATION TWO will give the same result. This ADC can simply handle both situations equally well. That's nice :-)

How is that possible?

If we look further in the datasheet we can read that the ADC uses a switched capacitor input. My guess is that when a sample is taken, a capacitor is charged to the input voltage. As long as the switches function over the full supply range (and that can be implemented easily with CMOS passgates), the capacitor will simply be charged to: V(AIN0) - V(AIN1)

Then the capacitor is disconnected from the inputs and the charge in the capacitor is determined. This can be done at the "internal" commonmode level so the commonmode level of the inputs is no longer relevant.