An answer to your question can be found here.
Advantages of ducted fans would be:
Better containment of broken blades
protection of ground personnel when the engine is running
Smaller size than a comparable propeller
They look like a fancy jet engine. This is probably the main motivation of Airbus for their use on the E-Fan.
For almost all ...
R W Hovey indicates Ducted Fans are more efficient below 100-110 mph, with 80 % propulsion efficiency (percent of delivered mechanical power that is converted to thrust), above this, a free propeller is better, 85 % efficiency from 200 to 300 mph, up to 400 mph, when it drops to 60 %, and is catched by turbofans, 64 % efficiency at 450 mph; above 500 mph, ...
The weight of the battery is mentioned here:
Power is provided by 127 kg. of 250-volt lithium-ion polymer batteries
from Kokam in South Korea built into the wing.
A slightly different weight is specified here:
... E-Fan has two lithium-polymer battery packs weighing 65 kg each.
I could not find which Kokam battery is being used on the e-fan, but ...
Slightly adjusting your energy estimate (3.6V × 40A × 120 Cells = 17280Wh vs original 19000 Wh), taking an energy density of 125Wh/kg for a high quality battery, it can be estimated:
which I think sounds reasonable for a plane with a empty weight of around 500kg.
The primary reasons you'd want contra-rotating pairs with conventional (unducted) propellers are cancellation of torque/P-factor, and delivering more power with a limitation on diameter (tip speed, usually, or landing gear height).
Neither of these really applies to ducted fans; it's easy to null out the slipstream rotation with fixed vanes in the duct, and ...
For a propeller/rotor, net consumed power = torque * rpm. For an electric drivetrain, net power delivered = current * voltage, with current equating to torque and voltage to rpm. Tesla should have really good data analyses on the power delivery as a function of demand over time, with wheel torque and wheel rpm as parameters.
Then you only have to replace ...
It's not easy to find research on small ducted fans. I did come across this interesting masters thesis from 2009, which does show some relevant results - at low propeller speeds.
The document describes three duct designs, one with a variable bypass inlet and two simpler ones. The simplest one is made from PVC tuning and a foam inlet lip: