The Italian communist party was founded in 1921 from the more radical members of the socialist party (which was founded in 1892), after the 2nd World Congress of the Comintern.

Did they have any kind of presence in Parliament before Mosolini?

The socialist party had a strong presence in the parliamente during the Kingdom, and in 1921 obtained 24,1% of the votes, while the communist party only obtained 4,6%.

Was there a chance of then flipping to the soviets side at any point?

This is a bit unclear. Are we talking about during the war? Because the communist party was aligned with Moscow since its creation. It was a revolutionary movement and they really wanted to bring forth a communism revolution in the country, after all. Palmiro Togliatti (secretary of the party between 1927 and 1934) even had a city in Russia nominated after him when he died in 1964.

In Italy it was officially outlawed in 1926, but already in 1923 some of its leaders were being arrested or threatened by the regime. So it was a clandestine organization actively trying to overthrow the regime.

Were there protests, slow downs, strikes of any kind during the war

The first strikes organized by the party were in march 1943, around 100.000 workers took part in them and were the first big strikes of the fascist regime, since they were obviously forbidden.

Since its foundation in september 1943, the Italian Communist Party, together with the Italian Socialist Party, the Action Party, Christian Democracy, the Labour Democratic Party, and the Italian Liberal Party was a member of the CLN, Comitato di Liberazione Nazionale, the main Italian resistance movement fighting against the German occupation of Italy in the aftermath of the armistice of Cassibile. It was a multi-party entity, whose members were united by their anti-fascism.
The Brigate Garibaldi, the bands of the communist party, were composed by more than 50.000 men and were the most numerous. Like all the other partisans brigades, they supported the allies during war actions and used guerilla warfare and sabotage to ambush and harass the nazi-fascist forces.

You might also want to check this coment about the Italian resistance movement: https://www.reddit.com/r/AskHistorians/comments/22xwz3/how_effective_was_italian_resistance_in_wwii/ch23zkh from u/haZyyskies

sources: anpi.it (website of The National Association of the Italian Partisans)
P. Ginsborg, Storia d'Italia dal dopoguerra ad oggi