Spain was neutral during the Second World War, though they did contribute a division of troops to be used on the Eastern front for a time. So, technically, Spain wasn't involved in WWII.

Now, in a way, you should have asked this question a week from now. I am joking, of course, but by then I should have finished with my current reading: Paul Preston's The Spanish Holocaust: Inquisition and Extermination in Twentieth Century Spain. There is an entire section on the post-Spanish Civil War period that begins on page 471 and ends on page 517, and this period covers Spain from the Nationalist victory in 1939 onwards. Sadly I am on page 261. It is clear that the Nationalist repression continued past the final day of the war. There were prisons, concentration camps, and ongoing repression of human rights. Martial law wasn't rescinded until 1948. The specifics are something I have only studied in passing, so I can't really give you a full rundown. I'm also not an expert on the definition of genocide, so I can't say if that word would apply.

I know those had similar ideology to Nazism

The definition of fascism is complex and debated. Some argue that Franco clearly fits their definition, others point out that his regime differed from other fascist regimes in several respects. He was certainly a rabid nationalist, a Catholic of convenience, a lover of the Army, and possessed the ability to suborn different factions to his own uses (Catholics, two different strains of monarchists, fascists, business interests, and others flocked to his banner, but most did not have their interests served in the end). He was also the head of a regime that José M. Sanchez described as 'barbarous,' a description I think is apt.

As for Italy, I will largely leave that to others to cover. There were Vatican efforts to mitigate the suffering and deportation of Jews, but the Vatican is a separate state from Italy. This is covered in depth in the recent book by Gordon Thomas: The Pope's Jews.

I hope that provides some answers to your question. Followup questions by OP and others are always encouraged!

Ruth Ben-Ghiat's Fascist Modernities and Claudio Fogu's The Historic Imaginary touch upon this issue. In short, Italy decimated 10% of the population in Libya through the use of gas and other arms before WWII. Italy has a limited post-colonialist history in comparison with other European nations. Mostly, they participated in post-colonialism to prove their "whiteness." Lucia Re of UCLA has a book coming out on the effect of race in the development of Italian nationalism. There were no death camps in Italy per say, which is why they've painted themselves as an Italiani brava gente (Good Italians). Even the Italian Jews supported this myth in order to be incorporated into the post-war government. In comparison to other Western European nations, only (as if "only" could actually mitigate the horrors) 44k Jews were sent to camps elsewhere. Jews were generally transported by train to death camps elsewhere. The Vatican's involvement in the situation regarding the Jews really only occurred towards the end of the war. Gordon Thomas's book has been debated and disregarded by many historians of Italian fascism.

This is probably bending the rules a bit, but I hope it's ok to present this radio documentary without much further comment. I apologize if this is not appropriate.

The Canadian Broadcasting Corporation ran this a while ago - it examines the notion that Italy was a relative safe-haven for Jews in Fascist Europe, and finds (based on recently released documents) that the notion of the "Good Italian", or that Italy was a safe haven, is false. It presents the idea that Italy and Italians were largely willing and active participants in the Holocaust.

Because of the fact that the relevant documents were only recently released by Italy, it seems likely there probably won't be too much scholarly work out there on Italy's involvement that takes this information into account. Hopefully there is some, and someone better informed than me can point to it.

http://www.cbc.ca/player/AudioMobile/Living+Out+Loud/ID/2417073339/