There is no written record anywhere of Mussolini raping Dorothy Thompson. Also, she was married to Sinclair Lewis at the time.
Mussolini discusses how they put down a rebellion in Libya. But Italian Libya would not exist until 1934, when it was formed from the merger of Tripolitania (centred on Tripoli) and Cyrenaica (centred on Bengasi or Benghazi). These were two territories captured from the Ottoman Empire. With the merger of these two in 1934 by Mussolini, however, Libya attained its approximate modern boundaries.
The assassination attempt is based on Violet Gibson in 1926. However, it took place outside, in a crowd, not while Mussolini was in his car as shown in the drama. Gibson had armed herself with a rock to break Mussolini's car window if necessary, and a Modèle 1892 revolver disguised in a black shawl. She fired once, but Mussolini moved his head at that moment and the shot hit his nose; she tried again, but the gun misfired. Gibson was almost lynched on the spot by an angry mob, but police intervened and took her away for questioning. Mussolini was wounded only slightly, dismissing his injury as "a mere trifle", and after his nose was bandaged he continued his parade on the Capitoline Hill. Gibson was an Irish woman who was severely mentally ill, and had come to Rome a couple of years before to commit suicide after converting to Roman Catholicism - although she is described as a "committed anti-Fascist" on a plaque in Dublin, her inspiration seems to have been more religious based than political. She told interrogators that she shot Mussolini "to glorify God" who had kindly sent an angel to keep her arm steady, although the angel did not stop the gun later misfiring. Mussolini granted her an amnesty, and she was returned to the UK where she spent out the rest of her life in a mental hospital. However as in the series, this incident greatly increased popular support for Mussolini in Italu.
It is a common trope that Mussolini made Italian trains run on time, and this is shown early in the series. Much of the repair work to the Italian railway system were done before Mussolini and his fascists came into power in 1922. Mussolini was just disingenuous in taking credit for all those changes, although his government did invest heavily in rail and road infrastructure.
Mussolini did not adopt his headgear and outfit arbitrarily as shown in the series after rejecting a number of suits, he based his look and that of his Blackshirts on the Arditi, an elite unit in the Italian Army in WW1. Contrary to stereotypes about the Italian military, they were highly respected and feared by their opponents.