This one is kind of complex.

Operation Barbarossa was the operation the Axis had planned to invade the Soviet Union. Nazi Germany had started to amass troops and equipment and had a pretty substantial force at the border in February of 1941. The original plan for the operation was to take place in May of 1941. There really was no shock, Stalin knew of the amassing of German troops and was warned by Soviet military leaders of an impending attack.

Mussolini and the Italian Military were fighting the Greco-Italian War in Greece and making no headway. This is considered the start of the Balkan Campaign. The stalling of Italy in Greece lead to Hitler start Operation Marita which was the German invasion of Greece, which coincided with the Italian invasion of Greece, which had stalled. Hitler had no intentions of invading Greece at this point, but was forced into action by Mussolini.

To sum it up quickly at this point. Italy tried to invade Greece from Albania, without Hitler and a lot of other important Italian leaders knowing, and failed. Greece actually pushed back and started taking ground in Albania. Hitler pushed forward with Italy to invade and defeat Greece.

The failure of Italy to defeat Greece on their own meant that some of the troops and materials for Operation Barbarossa were used in The Balkan Campaign. Which, with some other weather related issues lead to Operation Barbarossa being delayed. The delays are questionable at this point, there is some speculation that the Operation could have continued, even with the Germany military being deployed in Greece.

Prior to the entire Greek campaign, Italian forces under Mussolini had dealt with setbacks in the North African Campaign. Which lead to Rommel being deployed to Africa to aid the Italians in that campaign.

The relationship between Hitler and Mussolini was complex and stressed. Mussolini never felt like an equal and the invasion of Greece was not advised by Hitler, rather performed by Mussolini to impress Hitler. Which basically lead to Hitler having to bail him out. Hitler commonly didn't communicate with Mussolini, so not knowing about the invasion of the USSR isn't odd.

So to answer your first question. Mussolini already had his hands full with the Greco-Italian war. Aiding Hitler at the border of the USSR would have been near impossible. Hitler delayed Operation Barbarossa to aid Mussolini in Greece.

Anecdotally, I would assume that there was some irritation on Hitler's part with Mussolini. From everything I have read about the relationship between Hitler and Mussolini, Hitler never viewed Mussolini as an equal and Mussolini never felt like an equal. Even prior to any invasions.

So while both Italy and Germany had signed the Pact of Steel, both countries had trouble with meeting the obligations of the pact.

As to when did the Italians get into the USSR? The Italian Expeditionary Corps were deployed to the USSR in July of 1941. Later the expeditionary corps were upscaled to a full sized army unit in July of 1942

Operation Barbarossa had started in June of 1941, so the assistance of the Italian military had come less than a month after the campaign started.

Then you get into the whole invasion of Northern Italy. Hitler had basically set up a puppet government and put Mussolini in charge of Northern Italy after Southern Italy was retaken by the Allied forces. Mussolini and his mistress trying to escape to the Swiss border, being captured by allied Italian fighters, both of them being shot and then their bodies were hung in a park in Milan and defaced by many, many Italian citizens.

In general the two Axis powers did not have a productive or coordinated relationship. Though they'd bonded in the mid 30s over Abyssinia and Spain, Hitler never clued Mussolini on big decisions like the Anschluss with Austria or the invasion of Czechia, and cracks began to emerge as Hitler pushed for war in 1939. Mussolini had promised to stand with Germany when the time came, but he had anticipated a conflict in the mid 40s and when things got serious he had to tell Adolf that Italy wasn't ready. This was a big blow to Mussolini's prestige, made worse when the Wehrmacht bowled France over the following May. Italy's hasty and embarrassing declaration of war on France followed.

As a result, Mussolini started to look distinctly unreliable, and Italy a decidedly second rate ally. This made Hitler, never the most consultative person, even less likely to share major plans. In late 1940, envious of Hitler's triumphs and unhappy with Italy being sidelined to the North African theatre Mussolini decided to recapture some status by invading Greece.

This was a terrible idea that rapidly became an absolute disaster, not only because Italian troops got their arses handed to them by a smaller, poorer nation. It threw off the timetable for the North African campaign at a point where Britain was scrambling to defend Egypt, it as good as invited the Allies to send forces to the Balkans, it upset Stalin and meant that forces would have to be diverted from Barbarossa preparations. It was in this context that Hitler met Mussolini in January 1941 and gave no hint that he was preparing to invade Russia.

Sources:

Kershaw Fateful Choices: Ten Decisions that Changed the World 1940-1941, 2007

Kershaw Hitler 1936-1945: Nemesis, 2000

I can't answer your central question "why didn't Hitler tell him" completely, but here's some relevant context:

There wasn't a lot of consultation between German and Italian leaderships regarding plans for the war to begin with - when Germany attacked Poland (September 1st 1939), Mussolini had only known about the plan to do so less than a week before (August 25th).

Regarding plans to attack the USSR in 1941, the Germans couldn't expect much help from Mussolini's Italy anyway - the Italian military hadn't been prepared for a new war of aggression like the German had, and it was just going through a kind of consolidation phase (remember, the late 30s had been a phase of military activity for Italy, the Italo-Abyssinian War and the occupation in Africa as well as the intervention in Spain had already used up resources when Germany attacked Poland).

It's also important to consider how the relationship between Germany and Italy had changed between 1939 and 1941: before that, there was some kind of at least political and symbolic equity between the two regimes. When the war began, Italy wasn't ready for the kind of Europe-wide war Hitler wanted (to put it bluntly, somebody might want to add nuance to that).

• Italy stayed out of Poland in 1939,

• rushed into France in June 1940 when the Germans made visible progress, but showed a lack of military planning and equipment, losing lives and time for small and insignificant gains of ground in the Alps,

• started a war against Greece in October 1940, partly because Mussolini wanted to repair the damage to his and Italy's reputation that had come out of the embarassment in France (his standing as duce del fascismo relied partly on military success, which was an important motivator for him to rush into the next aggression despite the considerable strain already on Italy's military and also despite the Germans trying to get him off the idea);

• and lost out again and again against the British in Africa between December 1940 (in Egypt) and May 1941 (when Italy lost its colonies in East Africa).

That was Italy's military track record in 1941. Mussolini had attempted to lead a "parallel war" to Germany, and had pretty much failed. The balance within the Axis had shifted heavily towards Germany.

When the attack on the USSR began, the Germans (especially Keitel, the Wehrmacht's chief of staff) tried to convince the Italians not to send troops. They changed this stance only after their own war against the USSR had begun to stall. Hitler wrote a personal letter to Mussolini in December 1941 in which he basically greenlighted Italian participation in Russia. So regarding the second part of your question: Italy got into the war in Spring 1942 with up to 220 000 soldiers at one point, which is a considerable number regarding the circumstances. However, they weren't really equipped for the climate, didn't have much heavy artillery and would also not effectively work together with the Germans since German and Italian leaderships couldn't agree on combining command structures.

Sources: Wolfgang Schieder, Der italienische Faschismus (and less directly Brunello Mantelli, Kurze Geschichte des italienischen Faschismus). Both of these books are short oversight monographs, not extensive academic works (although both written by historians with a reputation for that specific topic).

I am currently reading The Skin by Curzio Malaparte which is a fiction but alledgely based on true experiences during WW2 when the Allied powers took over.

I found out his real is actually Kurt Erich Suckert and he is part german, he seemed to be a darling to one of Benito's newphews or something which got him out trouble, He also came from a lot of money apparently and lived a real charmed life.

I am wondering on what do people think of him, is he taken seriously, are his accounts grossly exaggerated? Did he have nefarious reasons for writing, etc....

The opening of the book talks about little boys and girls whoring them selfs out to Allied Troops and that Negro Allied Troops were unwillingly sought after for marriages for some odd reason I do not understand.

I have read some italians hate him and some hold him in high regard for his "honesty"....

Can anyone elaborate about this?

The book caters to his time spent as a journalist during WW2, I guess he was orginally set up that way by Tito but that he joined the allied forces during their win, he is typically in their company thus far in the book.