Documents for travelling within the Schengen region

I would include the rental reservation in the friend's name along with a statement by the friend about the travel plans. This seems implicit in the instructions:

car registration, car insurance

Rental reservation seems a reasonable substitute for these; if the driver will use his or her own insurance, include that, of course.

return travel tickets (ferry or Eurotunnel) mentioning the car’s registration number and driver’s driving licence.

If there's no ferry in your itinerary, omit this, of course. I would include the driver's license no matter what.

If applicant is not the driver, then driver’s cover letter (signed & dated) confirming joint travel with applicant and travel dates need to be provided too.

This should be self explanatory.

You asked:

If I understand correctly, showing documented proof for travel within the Schengen area is not mandatory and detailed itinerary should be sufficient as there are frequent trains and buses and it is just one of the supplementary documents. Is that correct?

Probably. Other evidence of plans in Germany should be sufficient to justify an application to the German consulate. Principally, this should include evidence of accommodation such as hotel reservations or a statement from someone with whom the traveler is staying. Other reservations can also help.

But if VFS is asking for evidence of your intra-Schengen travel before they'll accept the application, you have two options: either to provide it or to complain that it shouldn't be necessary. The first option is probably faster.

If you nonetheless want to complain that it shouldn't be necessary, VFS has a customer complaint procedure. They should escalate the complaint to the German consular service if necessary. If they do not, you should try getting in touch with the consulate directly to complain that VFS is using incorrect criteria to refuse to process visa applications.