Thanks @saturation. To answer your questions:
1.Yes, the grounding is done properly, the soldering tip and the hot air tip are both grounded (passed continuity test with the ground pin on the plug). And visually, the ground wires are screwed onto the case base with pressure washers, seems pretty good to me.
2. It is a bit difficult to measure the temp from the nozzle as the temperature changes quite a bit depending on where the measurement was made. But after playing around with the suggested measuring method using an Extech 430 (type K thermocouple) it seems that the temperature readings are about right (I only measured using the two nozzles with the larger diameters since with the smaller diameter ones it was pretty difficult to place the thermocouple at the correct distance accurately), it's around 10 degrees off (for my measurements it was around 10 F highter, but pretty consistently.)
3. The soldering iron tip temperature seems to be pretty accurate though, since the temperature adjustment only goes down to roughly 401F (205 Celcius), I couldn't test it with the 63/37 solder method. But the thermocouple reading across the range seem to be within 2 degrees of range give or take. I wouldn't put too much emphasis on the numbers here though since I am not sure my measuring method is accurate enough.
One thing I did find out while measuring the iron tip temperature is that there is a bit of a lag (maybe 10 to 15 seconds) between the time when the displayed temperature on the 7-seg display versus the time the soldering tip actually reached the temperature measured by the thermocouple. But I think this is pretty typical.