Compressor doesn't work

Sounds like overheating.

Sounds like a fuse has gone all fuses are under bonnet remove fuse lid on the back of the lid should be a cardboard fuse diagram telling you which number fuse does what

You have troubleshot this thing well. You may have a capacitor problem or starter problem. It will not be design let the unit come on. This is all to protect the expensive compressor.

since neither light is going on, then i believe that you either have a bad thermostat, or possibly that you only have half of the voltage going to it, and gaggenau doesn't have gas units so it doesn't have a glow bar like the previous guy said.

CHECK THE AC AND HEATER CONTROL FUSE.MORE LIKELY FUSE BLOWED BECAUSE AC COMPRESSOR COULD HAVE FAILED IF LOW SIDE IS OVER 100 PSI. THE REED VALVE PLATE IN COMPRESSOR PROBABLY DAMAGED CAUSED COMPRESSOR FAILURE BLOWED THE HVAC CONTROLS FUSE. HAVE AC SHOP CHECK IT OUT.

fridge settings numbers are the smallest number 1 is the coldest for the fridge
freezers or the opposite so 1 is the warmest
check the freezer door seals

Your rear turn signal flashes fast because the front is not working. Most likely you have a burnt out bulb in the front. If your A/C compressor can be turned over by hand and doesn't lock up or make any clanking sounds it's probably alright. The compressor will not run if the system is low on refrigerant. If you're having problems with the A/C and heater controls, that would be the first ting to repair. It doesn't sound at all like any electrical problems.

I would recommend having a dye test done. If was to guess where an undetected leak maybe would be in the evaporator core.

Take it to a metal scrap yard and turn it in the copper and buy a new one. Buy a different brand.
Sorry to be so blunt but dehumidifiers are very cheap and disposable not many people work on them. If this help please rate me and do a testimonial.