If you are using Rex, especially at full power, the fan will stay on when you stop, just as in an ICE car. I usually try to turn Rex off a few miles before stopping to avoid this. It is rather noisy and smells hot.
The EV Connectors EVSE will be OK and give you a noticeable improvement in charge time. With only a 40A main supply you certainly should not install a 32A EVSE. Here in the UK I believe a continuous load such as car charging should not exceed 50% of the main supply. We have a 60A main supply...
What was the error message that should have been displayed when the check light comes on? Probably you can't do anything about it, only the dealer who should be able to trace the fault.
The car does track consumption and electrical miles. I have the android app and it will give you the all-time m/kWh (4.3 for me) and the electrical miles. There may be hiccups with software resets on the consumption though. And you need to factor in charger losses etc.
Edit: Your consumption...
Interesting. I find just the opposite on range. Consistently better than the Gen1 Leaf by 5 miles or so even when using the heater in winter. (In the Leaf we shivered - in the i3 we just leave the climate control on all the time). Of course it may be that the i3 performance is tempting you to...
That's only the car's best guess. A full cycle will probably allow it to improve the accuracy. Also it's temperature dependent and 15C is quite low.
In any case 600Wh is only 2 miles range. My guessed range at full charge varies by up to 15 miles. Stop worrying and enjoy the ride.
It depends what state of charge you have when you start. You imply around 50% if you can do the return journey of a full charge, so an hours charge should get you up to about 80% which is below the point at which tapering starts. That hour should give you about 25 miles which corresponds to...
£1.50 or more seems to be typical for those that do charge.
Slightly off topic, but it should only take somewhat over 3 hours to fully charge at 7kW though it does taper down at the end.
4.3 m/kWh would give you just over 80 miles if the battery has its nominal capacity of 18.8kWh which agrees with the range estimator at full cahrge. But the indicated range is calculated over the last 20 or so miles of driving, so if your last few miles have required more energy the range will...
The error message suggests that the Lion battery is very low, but that the 12V battery is sufficient to boot the car. Maybe they did trickle the 12V, or boot up the car occasionally?