Hey
Yeah it's hard to see exactly what happens from a small drawing like that. There is no path down
through to the battery though, it's a solid adapter, the blue is just the insulator. The liquid will pool in the moat.
However, that was just the first design

As you say, it's better if the moat is much narrower and the outer rim comes part-way up the atty, like a chimney, then it will re-uptake the leaked liquid. That will be v2 I guess
The battery causes the coil in the atty to heat up, yes. Just like a polystyrene cutting wire, or a toaster. The resistance of the nichrome wire in the small coil is chosen so that it gets hot but not too hot. It will go to 300 degrees C or more if dry, but when wet stays down at 180 C or so. This is enough to nebulize the liquid, and it works exactly like a disco fog machine - the PG and/or VG causes water in the liquid and in the atmosphere to condense and form fog, which carries the flavoring and nicotine if required.
The 1st-stage vapor is reported to be about 66% water. The wire is chosen to have a resistance of between 1.5 and 5.2 ohms, depending on the application (mainly to suit the voltage, which can range between 3.1 and 8.4 volts). So it draws about 1 to 2.5 amps and uses 4 to 12 watts, most of the time. The more Watts of power, the more, hotter vapor you get.
Power in Watts is the most important value. Next would come the physical size of the atty coil, because in most things the bigger the better. In other words a big coil that runs at 8 Watts will produce more vapor than a small coil pulling 8 Watts. Same with most things, antennas, propellers, whatever. You can't change the laws of physics, Jim.