Try to put absolute path to your file name "Utenti.dat", e.g. "/var/www/cgi-bin/Utenti.dat" or whereever this file is.

Line to change: file_utenti=fopen("Utenti.dat","a+")

and ensure that the file is readable for everybody (chmod o+r Utenti.dat).

Actually the web server's default path is probably /var/www that is why it do not find your file in this path.