I RMA'd it and got a new one back today (S/N G6YE3260025R), after 4 weeks! The new one does not have the thick thermal pad that presses on the SSD. I this a design change or has somebody on the assembly line fallen asleep?
Anyway, the problem with the memory is solved. But problem 2 is still there: I only get HDMI output to my monitor with the standard Windows VGA driver. When I install the Intel driver and reboot, the screen goes black after the "starting Windows" animation, i.e. after loading the driver. Soon after that my monitor says "no signal detected". I checked monitor and cable on 3 other systems and it works fine.
The NUC does start up though, I can access it with remote desktop. I cannot find anything in the event log that indicates a problem with the graphics driver. But on every boot I get 4 warnings Event ID: 37, Kernel-Processor-Power , The speed of processor (0-3) in group 0 is being limited by system firmware.
Updating the BIOS did not help.
I tried to contact Intel Support directly, but the link Contact Support is broken. It says "error opening http://supportcontact.intel.com"