Dragos - I'm confused. As far as I know all Cayennes of the 958 series have HID headlights. At least in the US. Do you have a link to the Hella LED headlights?
You answered very well, and my problem was solved as well.Dragos - I suspect what you're calling Xenon is a high-intensity-discharge (HID) light source. This is basically an arc lamp (arc discharge between two electrodes). US 958 had HID "bi-xenon" lights, where the low and high beams were provided by the outside light source, using a shutter to block light for the low beam and open it for the high beam. The "flash" high-beam (triggered by pulling back the turnsignal lever (ie - "flash to pass") is a simple H7 projector. Those are only illuminated when the turn-signal lever is pulled back. The lights are self-leveling (a requirement in Europ for HID lights) and "Litronic" which implies some steering of the light beam in response to the steering wheel position. On US cars - turning into a corner turns on a separate light source in the headlight closest to the curve that points to that side of the car illuminating the corner. Later Litronic lighting also steered the low-beam light in response to road speed and curves.
As far as the internal components getting wet - that's surprising since they seem to be fairly well sealed, but it sounds as if something happened to yours there they're allowing water inside the housing.
I noticed the one listing you had for the LED lights said they were for right-hand-drive cars.. I'm not certain what side of the road you drive on but I'm going to guess that your steering wheel is on the left making it a left-hand-drive car. It would be worth checking this with the vendor I imagine.
To answer your question on the bulb-out warning, my guess is Hella has taken this into account in the design of the lights - I can't imagine they don't - and it would be an issue. It certainly might be wise to contact Hella to confirm this before spending that much money.