Max voltage vs current for LED
The trick with diodes is they have an exponential I-V characteristic.  This means that the current flowing through has an exponential dependence on the voltage, and past a certain point very small changes in voltage result in very large changes in current.  The resistor basically serves as feedback, relating the voltage and current with a better-behaved linear relationship that is less sensitive to changes in voltage (linear instead of exponential).  The exponential characteristic of a diode can be modelled as zero current until a thresold voltage is reached, then a constant voltage drop.  Below the threshold, the diode is turned off ('in cutoff'), and above the threshold it will be forward biased.  

If you put an LED in parallel with a zener diode, most likely no current will flow through the zener diode (it will be in cutoff) and all of the current will flow through the LED.  This is because if you try to put more than 2v across an LED (assuming the forward voltage is 2v), you will get a very high current flow (amps, not mA) which the resistor will limit with a large voltage drop.  So the circuit will end up stabilizing with 2V across both the LED and zener, but with little current flowing through the zener.  You won't damage the LED so long as the resistor limits the current to something the LED can handle, but the zener will do nothing.