HI mate BEC means Battery Eliminator Circuit , some ESC like afro dont have power for receiver or FCB so we use the bec to gives us normally 5amps at 7-9v
As for props to motors a 3 cell will turn motor at given rpm per volt so if you then give it 4 cells it will have a higher top end as there is more volts being put in you just have to make sure if motors are 3 cell rated they dont over heat , it not to bad on a quad as they are in the airflow so cooling is good , even better if you find a 4 cell motor