LED is not a resistor, is a diode that is a non-linear device. The current flowing through it increases exponentially with the voltage across it. To connect it to a power supply you need an external resistor that limits the current at the wanted value.
If you know, from data-sheet, that at a voltage drop (across the LED) Vd the current will be Id and you want to connect it to a power supply Vcc, then you need an external resistor R = (Vcc - Vd)/Id. In this way the current will be Id in both LED and resistor. You will have a voltage Vd across the LED and Vcc-Vd across the resistor.
The answer at the second question depends from many factors, the power supply could also be damaged.