Doesn't this equal a registration with the authorities? I mean they have the name of the buyer, of the dealer and (i suppose) the firearm he's willing to buy
In theory, no. The agency that conducts the check is not permitted by law to maintain a record of the background checks. What they DO have is the names of the buyer and dealer, and type of gun- long gun, handgun- but not the specific gun. If I am buying a Beretta 9mm pistol, serial number 123456, when the dealer conducts the background check, he has my name, address, date of birth. The checking agency knows it is for a handgun (you can buy rifle/shotgun at 18, 21 for handgun). They do not have that it is THAT Beretta.
As far as a determined person getting a gun- during WW 2, the Japanese had occupied the Philippine Islands. Islander made guns from water pipe, used a cigarette to fire them. In Warsaw, Poland, the Nazis had shut down the Jewish Ghetto, and were shipping Jews to extermination camps. Despite being surrounded by German military, they were able to smuggle a few rifles, pistols, etc into the Ghetto- when the Germans decided to clear the ghetto, it took over 2000 troops a month to do so.
If THEY could get guns, anyone can get a gun. If you have basic metalworking skills, you can MAKE a gun. There are towns of gunmakers in Afghanistan that make firearms with hand tools.
It is rather ironic that you have the restrictions that you do- when the oldest operating gun maker in the world is Italian- Beretta.