Flight training starts only after the student has been notified to the aviation authority (at least in my country)
Not a requirement of the EU Regulation.
As far as I can see these flights are advertised by the individual PPL and conducted independently of and without any reference to a flying school.
There are plenty of these but they go under the heading of Cost Sharing, not to be confused with Intoductory flights carried out under the auspicies of an organisation. One pilot recently convicted is doing three and a half years behind bars!