What information on a specific flight can be retrieved? I would like to know where and what to search in order to have information on a specific flight (i.e. scheduled departure time, real departure time, technical failures reported, etc.)

I'm guessing that this information can be found :
in the airplane's log
at the control tower (or the aeronautical uthorities)

Can you please tell me more about all this, especially the technical name of the different documents and the information contained within?
flightradar24 takes as input mainly ADS-B data, as explained here. It seems to be enough to know scheduled departure and arrival time, departure and arrival airport, registration number and some extra pieces of data you may not need.

For technical failure, you may see the aviation herald website (I don't know how to access ACARS messages)