1. Which is the right project to get started with loading my custom scene files?
This depends on what your scene files contain and what you want to achieve. The examples aren't designed to be generic POD viewers and are often tailored to work solely with their own POD file so the code is as simple as possible for learning the API/technique that they're demonstrating. For simple scenes that contain texturing, lights, cameras and animation then IntroducingPOD is the place to start. If you want an example that demonstrates Skinning then Skinning is the one to use as a reference. As you've seen, they may require altering to suit your scenes.
2. Which export settings do I have to apply in PVRGeoPOD so the .pod works with that project?
The answer to this is simply, the same settings used originally. These are stored in the POD files themselves. The best way to use the original settings is to import the POD file as an options profile (right-click in the profiles window on the exporter). Then set the new profile as the current export options.
3. Which properties are obligatory for my .dae file (Do I need textures in every material? Do I need to include a camera / a light?)
This can vary from example to example but for IntroducingPOD it expects a light, camera, vertex position, normals and texture co-ordinates. It also expects that the latter 3 are using the data type float.
FYI, looking at your error I'd guess that your simple cube is either missing texture co-ordinates or when you exported it the "Export mapping channels" option wasn't enabled.
the hint with the POD file options profile was especially helpful.
In this context I have a suggestion from my user-perspective: it would also be very helpful if the original .dae files were included in the demo projects instead of the (proprietary) .max files. That would have permitted me to mimic the respective dae’s structure when trying to get my own models to work.
Do you happen to have a suggestion where to find a more generic pod loader project?
That would really facilitate getting started with the SDK.