BEC means battery eliminator circuit.
A BEC generally provides a reduced voltage to stuff that doesn't need or cannot handle the full voltage of the battery. In 'our' case of multirotors, the flight control board, receiver, servos, some cameras, etc., don't require or need 12V, so a 'BEC' reduces the 12v down to a manageable voltage, generally around 5V. Many ESCs can do 2 jobs. . . provide reduced voltage to stuff and switch direct current to alternate current for brushless motors or a BEC ESC.
And without going into the minutia of
www.ecalc.ch or F=MA stuff, what can handle 3S (10v-12.6v) or 4S (13.3-16.8v). . .generally it says on the component specs. As in
this wonderfully cheap and great ESC. . the third line down in the specs tell you 3S-4S Lipo. Or
this motor can handle both 3S and 4S as it says beside battery in the specs.
And in general higher KV motors spin smaller props and visa-versa. Higher KV motors generally cannot lift as much mass as a lower KV motor.