Why is there a gate-source short on the n-channel mosfet? (circuit attached)
Check that the flyback diode is installed with the correct polarity. 

That is the only thing I see that would explain all three of your observations. 

The MOSFET getting hot would be due to excessive current. You have enough gate drive voltage. 

Gate-source short could be due to overheating of the die. 

The LED going out could be due to the diode melting inside into a short or due to MOSFET damage. It's only a 1A diode and that MOSFET is quite capable of driving enough current to get sufficient forward voltage to light a red LED (some tens of A or more).



Incidentally, it's important to check the actual PCB and part and not just the silk screen vs. component, because it's possible to get the mapping from schematic symbol to footprint wrong, especially the first time you've used a newly minted symbol-footprint combo.