Electronic – AS8510 ADC Reading to Current/Voltage Measurement

It all depends on what you are trying to calculate - if you are trying to calculate AC RMS values then having your software continually calculating the mean value of the two signals and using that in the RMS calculation gets rid of those pesky dc offsets and offset drift with temperature.

This just leaves you with gain calibration and this can be tricky if you haven't got highly stable potential divider circuits - I'd start by picking resistors with a 10ppm/ºC temperature coefficient - this then gets rid of that as an error but, your ADCs will have gain and non-linearity errors and these might drift with temperature. How you would counter these temperature effects could mean you ditching your current ADC and using a better ADC with the performance you want/need.

If you are wanting to measure dc levels then I'd use precision resistors and much better op-amps of the "zero-drift" variety AND design your hardware so you can do a "zero" measurement - you'll need analogue switches to do this and you'll need to do it on a regular basis.

It all boils down to what you want to measure and how accurate you want to be; neither of which are stated in the question.

...as far as i have read about them (also their data sheets), if an ADC has both single and differential ended inputs, we can use it as a single ended input ADC OR we can use it as a differential ended input ADC. Which means we cannot use it as both single and differential input at the same time.

This is not always true. For example, I have used ADS1015 on a couple of projects recently. On this chip, whenever you switch the channel being read you also have the option to switch between single-ended and differential measurement. (This is not an endorsement of this chip for your project. Just an example of a chip that doesn't have the limitation you thought was universal)

Furthermore, even if you had a device that had to be configured as single-ended or differential for all channels at the same time, nothing prevents you from using ground as one of the inputs to a differential channel. So you could just configure it as differential and move on with your design. The only thing you'd lose is the opportunity to use the 4th input pin for some other purpose.

Another option, if you plan to use external signal conditioning, you can do differential to single-ended conversion in the signal conditioning circuit, and your ADC will never know the signals are anything but single-ended. This essentially makes the amplifiers shown in your diagrams to be external devices rather than internal to the ADC chip (and add some filtering in their feedback networks to reduce noise).