Joerg, please let me explain briefly the first point, and leave the others to other participants, for brevity.
Body cavities act as resonance chambers for the sound coming from the vocal cords. These chambers react to different frequencies, best to certain range and less efficiently to others. As the frequency (pitch) raises, different resonance chambers are stimulated and others de-stimulated, producing the impression that the sound comes from chest first, then from head. So, it is the shape and size of the skeleton and consistency of soft tissues that determine the sound, rather than the singer's desire. Though a well trained singer can manage this to some extent, in general the result are dependent upon the physical characteristics of the individual.
For example, a tenor will find that some notes are definitely "chest" and others definitely "head", with a small interval in between, called the "passage", which may be from E to G in the upper lines of the staff . As my teacher says (he's a professional opera singer), DON'T worry about where your passage is. Just keep improving quality across the full range.
Un abrazo - Andrés (in Buenos Aires)