I mean, the Socialists basically had the run of things for the first 30 years of that state, and for some time before. They never went full Communist, sure, but I don't think they would have even with an alliance with the Soviets, at least if they wanted to maintain democracy. Communism and democracy don't usually make for good combinations.
Just to put something in perspective: when Ben Gurion needed to form his first governing coalition, and considered his options, he said "no Herut, and no Maki." Herut was Begin's right-wing party, one of two that would merge to form Likud (the other, the Liberals/General Zionists, was not beyond Ben Gurion's pale); Maki was the communist party. That's how much he hated the communists.
To put things even more in perspective, Ben Gurion had a choice of three partners for his first coalition: to his economic right, the Progressives and the General Zionists; to his left, Mapam (later one component of Meretz); and to the religious direction, Mizrahi (later Mafdal, now Jewish Home). He chose to go into coalition with the religious folks, because ew capitalism and ew Mapam. Kibbutzes split over the Mapai vs. Mapam question; members of the same family would not speak to each other if they were on different sides of the split. We're talking Judean People's Front vs. People's Front of Judea levels of schism here, except one of them actually ran the country for a couple decades.
The economy was pretty intertwined with the state already. In fact, I don't have solid figures for this, but I think it was Bibi's somewhat successful tenure as finance minister in 2003-05 that really turned this pattern around (an unusual thing about him politically is that he seems like a true believer in the free market, something most Israeli politicians are not), even though Likud had been in power many times before.
No, not really. The bulk of the restructuring was done in the 1980s, under national unity governments, as the state came out of hyperinflation. The biggest change, the Arrangements Law, which lets the finance ministry veto any government spending it thinks will raise the deficit too much, was enacted when Peres was prime minister in the 80s.
Government spending as a proportion of GDP has indeed gone down since 2003, but around half of the decline was related to the business cycle - in 2003 Israel was in a recession, and as it came out, welfare spending and such went down. Using 2000 as a baseline, government spending has gone down from around 48% of GDP to 41-42%. This contrasts with 70% in the 1980s.
See some information
here, and recent (since 2008) GDP and government spending data if you play with the table
here.
I think maybe the Soviets might not be willing to let emigration happen, but I DO think that exile could happen. Stalin notably hated the Jews, and was considering some action against them before his death. Exile to Israel might have been an option. Of course, Israel taking in millions of Russian Jews IN ADDITION to all of the Mizrahi Jews they were getting at the same exact time might be something that cripples the state and its institutions.
In the 1980s, Ashkenazi pundits were salivating over the upcoming Soviet migration wave, since they expected it would bolster their numbers over the Mizrahis. From the early 1950s to the early 1990s, Israel's Jewish population had a clear Mizrahi majority. It was also Israeli policy to encourage Jewish immigration whenever possible, to bolster national demographics. The IDF needed warm bodies; it wasn't until after it won the Six-Day War that Israel was convinced of its invulnerability.