Electronic – Use BBB analog inputs with 0..5V or 0..10V

Differential voltage means exactly that - the difference of the two input lines (Vin+/Vin- and Iin+/Iin-). The CS5463 can measure up to 250 difference between them (or 50mV with a higher gain). Both signals are referenced to AGND, and can range from 0.25V below AGND up to Vref (max. 2.5V). This is stated on page 7 in the data sheet (the maximum rating are a little bit higher, see page 13).

Your first question is answered partly in the explanation of your example circuit (Figure 18 on page 41). The data sheet says In this type of shunt-resistor configuration, the common-mode level of the CS5463 must be referenced to the line side of the power line. (Though it doesn't state why). One reason might be that you then don't need to break the neutral wire (which should not be done, neutral should be as close to earth as possible).

If you revert the plug, nothing bad will happen to the circuit - as long as you isolate any outputs. When you interface with other circuits which might be ground-referenced, you can create short circuits. Depending on the cabling of you house and the appliance you want to measure, you might trigger a RCD. (I'm not an expert here, hopefully someone more knowledgeable can explain this better)

Your resistor calculation seems OK. The input voltages can actually be higher that 250mV, it is just that this is the maximum voltage you can measure (anything higher will read as 250mV). So if you want to be able to read higher voltages (where I live we have 230Vrms) or detect over-load conditions, you should leave a safety margin (50mV seems fine).

The filter are connected to ground because you have different kinds of noise. You might have noise only on one line, or on both lines. For the voltage input, I would size Rv- like R1, and for the current input significantly larger than Rshunt. Then the capacitors can be sized to have a cut-off frequency of several kilo-hertz, so you won't influence the measured signal. You might also want to look at the evaluation board schematics. There are examples for the values (though it's schematic looks a little bit different).

1. Although a passive solution is possible, often depending on your source impedance and ADC input impedance, it's usually a good idea to use an opamp for the level/gain shift. One option is an inverting circuit such as this:

   

   Simulation:

   

   The benefit is a very low output impedance to drive the ADC (many ADCs require a minimum signal impedance of <10kΩ)
   The input impedance is just R3 (133.2kΩ in this circuit) To prevent loading effects, you want your signal impedance to be less than 10kΩ or so. If it's higher, you can increase R3 and R2 to increase the input impedance (as long as the ratio remains the same, so does the gain)
   Some opamps don't like a gain less than 1, so you need to check the datasheet to make sure it will be stable in this configuration. Also a small capacitor across R2 is usually a good idea to control bandwidth appropriately.

   The readings will be inverted, but it's easy to correct for this in firmware.

   A quad opamp with a decent voltage reference IC and divider to provide the 735mV reference for all non-inverting inputs could be used. The opamp must be able to swing its output down to ground; some op-amps cannot do this, so check the datasheet.

2. For the I2C and MAX127 (which looks fine) option, you could use a level shifter IC to convert between the 3.3V and 5V levels needed. There are quite a few such ICs designed for use with I2C. Have a look on Farnell, or Mouser, Digikey, etc. The PCA9306 is one example.

3. SPI uses "standard" outputs which are driven high/low (as opposed to I2Cs open drain) You can also easily level convert this, since each line is only one direction. A couple of transistors can be used.