What is the energy in "electron-volts" of an electron that has risen though a potential of 3V?
3 electron volts

Some definitions:

Energy, usually measured in joules, can be calculated as E=QV, where Q is charge, and V is voltage.  

Voltage is a measure of how much energy each electron has. It is usually measured in Volts, which are joules per coulomb. 

Charge is measured in coulombs, defined as the charge on 6.2415×10^18 electrons.  

These are good units to work with for practical electronics.  But if we're working with single electrons, those factors of 10^18 make the maths a pain. So we look for some alternative units which might be easier.  For charge, it's obvious - the single electron charge.  Volts we keep.  So that gives us a new definition for energy, from E=QV, the electron volt.  1eV is 1.60218×10^-19J.

So the question boils down to: "what is the energy gain of an electron which has moved to a potential 3V higher".  It doesn't really matter where that energy came from, in this case an electric field.  E = QV = (1 electron charge) × (3 volts) = 3eV.