Explanation for: A monopole antenna must contain a resistor (or equivalent) and therefore must have 2 terminals?
All antennas have 'radiation resistance'.  Power 'consumed' by the radiation resistance is actually being radiated away by the antenna instead of being dissipated as heat in a normal resistor.  Now, in order to dissipate power, you have to have both a voltage difference and a flow of current.  You can't do either of these with only 1 terminal.  

For a monopole antenna, one terminal is at the bottom of the antenna and the other one is on a ground plane.  The figure on the wikipedia article on monopole antennas has a nice drawing of this that also answers your symmetry question:



The 'symmetry plane' is simply a plane that you can draw between the two halves of a dipole antenna so that whatever is on top of the plane is the same as what is on the bottom of the plane.  A monopole antenna simply sticks a ground plane in there and deletes the bottom half.  I suppose you can also draw a symmetry plane vertically through a dipole as well, but the electric field is not tangential to a vertical slice like that so you can't replace it with a ground plane.