The movie is loosely based on a real story of Rubino Romeo Salmoni, Italian Jew who was kept in Fossoli Camp and later moved from there to Auschwitz (as 700 other Jews). Luckily he managed to survive the war and passed away in 2011 at the age of 91.
Italians, being on Axis side, could follow their own politic about Jews. There were concentration camps and restrictive law against Jews all over the country, but in contrary to Germany, Italian politic didn't envisage mass extermination.
In July 1943 Allies invaded Italy from the south and the Fascist regime collapsed. This paradoxically caused the situation of many Jews to become worse, because in consequence, Hitler took over the north of the country, Mussolini came out of prison and Italian Social Republic was created.
Concentration camps in Italy were used both for Jews and politic prisoners (as in many other places) as a work camp or a temporary place. The Sicilian camp in Farramonti, which was the biggest from all 15 internment camps, thankfully was taken by Allies at the beginning of Italian Campaign.
But from the camps on the north, that were took over by Germans, many of prisoners were transported from there to further camps in other countries, in order to die. Also many Jews have been killed in the camps in Italy. For example, as Frediano Sessi writes in his book Non dimenticare l'Olocausto, on 12th of July, 1944, 67 Jews and political prisoners were shot in the already mentioned Fossoli Camp.
The worst situation was in Risiera di San Sabba. The same source describes that those Jews who couldn't been transported to Auschwitz, were killed at the place. Together with politic and war prisoners, there were 3000-4000 people killed. In this aim there was built special crematory connected with 17 death cells, in which prisoners were killed with car exhaust, after torturing.
This way I find the movie quite reasonable, speaking of historical accurateness.
As for the second question about the percentage of Italian Jews killed during II World War. Depending on the source, there were only 40000-44000 Jews in Italy before the war, which is a very small number in comparison to other countries. Around 7500-8000 of them were killed, what gives 15-20 percent. Here and here you'll find the tables comparing particular countries.