The REFP input in the schematic has a voltage divider, so the input voltage reference will be divided before go to the ADC REFP pin.
Regarding the second question, the Arduino Expansion Board was designed to be powered through the barrel jack or through the USB port. You could use a plug like this one if you want to power the board with a battery: https://www.google.com/search?q=battery+barrel+jack&espv=2&biw=1600&bih=772&source=lnms&tbm=isch&sa=X&ei=tXDKVJXeIJPioAT…
However, I suppose you are taking about the J2 header, is that right? If so, that header is for attach a battery, but it will act as a backup power only for the Edison module when the main input power isn't present. This backup input power only prevents Edison module to shut down.
Good explanation, i understand all question.
If someone have my same objective i'm going to explain my workaround:
Connect the battery to J2 header, cut the 5V trace on expansion board and connect the battery + to 5V output in power header. I'm using an external stepup (TPS60110) to gain 5V from battery.
5V is big trace that run under POWER and ANALOG IN label of power and analog header.