The diode is probably OK. If you measure it out-of-circuit (removed from the circuit board) using the diode test range on your multimeter, with the black probe to the cathode (stripe end), you should get a reading of around 0.5~0.7V. 0.583V is fine. This voltage is called the "forward voltage" of the diode, and it's the voltage drop across the diode when it is "forward-biased", i.e. conducting.
You can also measure the diode on the resistance range of your multimeter, with the probes reversed - red probe to cathode. It should read open circuit (usually this is shown as something like ".0 L" or similar on the display).
It's hard to tell whether the 4011 is damaged just by looking at the pin voltages. I think it's very likely that it is, though. When you replace it, fit an IC socket, and buy a few spare 4011s, so you can replace it again if necessary.
U1 is the circuit reference for the 4011. Every component has a circuit reference - R1, R2, C1, D1, etc.
ESD is
electrostatic discharge. CMOS inputs are easily damaged by very small currents that are generated by voltages that build up on your body, often due to friction (your feet on the floor or on carpet) or certain types of clothes (wool and synthetics). It's possible to build up a charge of hundreds or thousands of volts. Sometimes you will feel it discharge - there's a spark and a pinprick feeling - but not always. These discharges are FATAL to CMOS inputs.
When you're working with CMOS, it's recommended that you wear a wristband that's connected to earth through a high resistance. This keeps your body at ground potential. If the circuit is also kept at ground potential, no electrostatic charge can build up between you and your circuit. Alternatively, you can cover the IC with aluminium foil, or conductive foam, while you're working on the circuit, to ensure that no voltage can form between any of its pins.
Look up ESD using Google or Wikipedia for more information.
