Electronic – Differential amplifier with common voltage far above the rail

I'm not 100% on this but I think most PIC ADCs are 10 bit (1 in 1024 resolution) but can have up to 10x LSBs inaccuracy - this means you're just about at the 1% accuracy stage without considering resistor accuracies.

Using PIC outputs as pull downs isn't a good idea either because there will be leakage currents from the pins that will add/subtract a voltage from the signal via the resistors. Also, you appear to be relying on PIC outputs going exactly to ground but neither is this the case and your accuracy on the lowest range will be dented.

Also, I think the zener won't be needed because R1 will limit current into the op-amp and it will self protect - 50V across 50k gives 1mA and most op-amps are capable of dealing with this sort of current using their internal diodes. I'd run the op-amp from 5V too - this means there's no chance it can stuff a killer voltage (6V or above) into the PIC ADC pin. Use something like an AD8605 - it is rail to rail but, because you can't exactly achieve 5V, scale things down by 10% and restore in the CPU with a frig-factor.

Having an op-amp that is self-protecting (due to the 50k) means negative voltages are also protected against but read the data sheets on the op-amp to be absolutely sure. If you still think you need the zener, consider that a zener will be starting to draw current at voltages significantly below 5V - it isn't an on-off thing as soon as you hit 4.99 volts.

A very simple reason might be that the differential pressure sensor might be wired backwards and this will cause the AD622 problems on the output without a negative supply: -

The output of the AD622 will swing somewhere between the neg and positive supplies but it won't get very close to them. See the box I've marked in red - it's saying that if your neg power supply is 0V, don't expect the output to get any lower than +1.1 volts in normal circumstances.

The smallest magnitude negative supply ought to be about -1.8 volts to be sure of being able to reach 0V cleanly on the output.

I suspect for your 2nd question that this is all about what happens when the pressure is too big and ch1 on the ADC cannot read it any more - at least ch2 can be relied upon for some readings even if they are subject to a few small extra errors due to resistor tolerances.

For question 3 - I'd like to see a circuit diagram.