This answer will be on Italian fascism and Turkey, so any further additions are welcome. I would like to also thank you for giving me the opportunity to tackle one of the main research questions of my PhD project...

Turkey's view of fascism during the 1930s is a very complex matter. On the one hand, certain fascist practices and laws were imported from Italy. These included the notorious articles 141 and 142 of the Turkish Penal Code, imported wholesale from Italy, with which all organisations on an avowed class base or that prioritised one class over others were banned. Similarly, certain elements reminiscent of Case di Popolo or, with some stretch of imagination, of dopolavoro can be found in Turkey at the time. Other influences include the reorganisation of the youth groups, the unification of nearly all NGOs under the umbrella of the Party, and so on. So it would be wrong to say that Turks, including Atatürk, hated everything about fascism.

The complexity begins with the fact that this very same sentence could be extended to the USSR. Turkey under Atatürk imported certain economic techniques from the USSR, in addition to acquiring Soviet expertise and technology in industry and military at times. Yet, it is so clear that Atatürk was not a communist, for why else would he keep persecuting the members of the Communist Party of Turkey? Clearly, he, just like other Kemalists, believed that certain things in the USSR could be beneficial in Turkey and could be separated from their ideological baggage. Adopting a 5-years plan did not mean that Turkey was communist, therefore.

While the literature on this subject is divided, with some more sociologically-minded scholars seeing Kemalism as a sort of unique, Turkish fascism, I would say that Kemalists perceived fascism in a roughly similar manner, Atatürk included. The borrowings from fascism are, as before, probably more 'ideological' than the Soviet economic plans. However, it is equally important to realise that Atatürk was declaring Turkey as a society where classes were not differentiated enough to allow class-oriented politics during the Turkish War of Independence (1919-1923). Even the Unionists in the late Ottoman Empire made the very same point. Therefore, the importation of the articles 141 and 142 were more about this established viewpoint and the Italian law best corresponding to it than an infatuation with Italian corporatism or fascism. It should also be added that the commissioner in charge that oversaw the translation and implementation of these articles was Fuat Sirmen, a man who became a doctor of law in the University of Rome. The potential impact of his past in Italy too must be investigated further before saying the final word on this.

On propaganda, this becomes even more obvious. In the 1930s, many Turks were sent or went by themselves to Italy (also to the USSR) and were quite impressed with the propaganda machinery used by the state. The backdrop here is the context of the Great Depression of 1929 in Turkey. As the Italian historian Renzo De Felice so brilliantly explains, the Crisis of 1929 was felt less as an economic crisis and more as a general, civilisational, moral crisis of the West, democracy, and capitalism. With Turkish economy harmed and with the formation of an opposition party in the 1930s turning to shambles (with an Islamist rebellion in the town of Menemen in December 1930 apparently being related to the new party's emergence), Turks decided to question what went wrong. Their answer (not wholly untrue at all) was that the Kemalist regime was insufficient in the propaganda methods it employed. The usual comparisons were the methods of propaganda and the youth organisations in Italy, the USSR, and Germany (roughly in this order of importance). Granted, some Turks were actually aware that the Italian case was not what the regime showed, as a report in the Turkish state archives describes the youth organisation of fascists as pretty much far less disciplined than portrayed by the regime. Nevertheless, it was quite clear that Mussolini did manage to create significant consent around his regime.

Another common point the cited countries had was that they all strived for creating a new man, a new society. Granted, the new man of Hitler was very different from that of Stalin. Yet, all had to change something that was and employ some techniques to establish the society to come. By contrast, the UK or France were perceived as more or less lucky exceptions in the history of mankind. In a book (Vatandaş İçin Medeni Bilgiler [Civil Information for Citizens]) dictated by Atatürk to his adopted daughter, Afet İnan, we see this clearly, where Atatürk argues certain electoral regimes could work reasonably well in nations that were mature enough. Turkey was not one of these nations, not yet at least, Atatürk believed. The old was being dismantled and the new was just emerging. For this reason, in the book, we see Atatürk observing that the 1924 electoral reform in Italy which allowed the domination of the Parliament by one party was a positive development, since the elections of 1919 showed that Italy was not mature enough to have a different kind of electoral regime.

The whole part until now shows two things. First, Turks, including Atatürk, did find certain things useful in the way fascism was applied in Italy. Second, with varying levels of enthusiasm (seems Atatürk himself did not care too much for it) they thought fascism was a relatively suitable system for Italy.

On the other side, you have someone like Recep Peker writing that nobody could claim that Turkey was a dictatorship or fascist, despite the fact that Peker himself was among the primary authors of much of the things described above. We know that Peker found himself in trouble with Atatürk at times, on which, some sources tell, his enthusiasm for Italian, German, and Russian 'inventions' was influential. Still, unlike some other countries at the time, even Peker did not think of Turkey as fascist, nor of fascism as something to be imported. It could be good for certain countries under certain conditions but Turkey was not one. Kemalism was enough for Turkey. Moreover, some sources tell us that Atatürk thought of Mussolini as an excellent Minister of Public Works. Meaning that in his eyes, Mussolini was quite good in draining the swamps in Italy (something almost universally applauded at the time, for some reason), but beyond that, his Prime Ministry was not even worthy of a mention. We cannot be sure about how true this is exactly, of course, but it is an important report that might well be true.

We have a particular reason to think that despite all that's been said above, Atatürk himself disliked Mussolini and fascism. The reason is that Atatürk criticised the Ottoman sultans for pursuing a policy of conquest that ultimately amounted to nothing but personal gain at the cost of much Turkish blood spilt. Similarly, he was critical of Napoleon's policies and rather than seeing him as a hero, he thought of Napoleon as a sort of megalomaniac (notwithstanding his intelligence) who implemented imperialist policies for the sake of his own gain. Incidentally, Mussolini was very often likened to Napoleon. With the additional issue of the ever-present Turkish suspicion vis-a-vis the Italian foreign policy during fascism. Time and again, Turks felt that Mussolini was a sort of Italian Napoleon bent on attacking Turkey for his imperialist designs. Naturally, even those who were full of praise for Mussolini's internal policies could not but feel disturbed by fascism's foreign policies. Especially so for Atatürk, noting his dislike of the Napoleon type as well.

Whether the remarks on Mussolini being an excellent Minister of Public Works are genuine or not, we can safely conclude that Atatürk himself was not fond of Mussolini or fascism for the reasons outlined. The Turkish interest in fascism had mainly two facets, with one concerning fascist propaganda and methods without much concern for their ideological content and the other fascism being a suitable ideology for Italy. When it came to foreign policy, the view on fascism and Mussolini became much less accommodating, both for Atatürk himself and for others. The key here is that though Atatürk was a soldier from the beginning, he did leave the Army once he became the President and followed a strict policy of keeping military affairs separate from politics. I always find it ironical that when he was putting away his uniform never to be worn again, someone like Mussolini or Hitler with military experience of just a few years were wearing them. Though all were nationalists, they were not all 'militaristic' in the same sense, to refer to your original question, and I think a significant part of the Turkish-Italian relations during fascism and Kemalism was influenced by this dislike of the overly-militaristic and aggressive (at least perceived to be so before and especially after the war in Ethiopia) foreign policy of Mussolini.