Additional battery required. It's possible to combine the whole thing with solar panels on the roof, but you need a good surface area to compensate for the use of the battery. As the battery dedicated to the wave 2.0 doesn't seem to have panel 'management', I'd go for an ecoflow battery that could be used for something else.
As far as the hoses are concerned, you need 2 connected to the outside. On some vehicles, there's a valve at the back that opens onto the rear bumper. I saw an installer at the camping show in Bern who was evacuating the hot air through this (Clim mode). As far as the air intake is concerned, I wouldn't recommend coupling it to the vehicle ventilation and creating a separate air intake.

Basically yes.
But you have to buy the additional battery
to buy. The additional battery can be
be charged at the cigarette lighter but that would never be enough
to run the air conditioning,
when the battery is empty.

You have to take at least one
hose from the vehicle
out of the vehicle. (per the supplier 2)
H.B.

This will be complicated because you'll need to install the air intake and exhaust ducts to the outside of the vehicle. Then you'll need to add the battery that attaches to the underside of the air conditioner for 12V operation.

Yes, that's true.