1. Why did the Soviet Union consider its domination of Eastern Europe to be of vital importance?
Why USSR Dominated Eastern Europe:
Pohnpei397's answer gives you the main reason. Here are two more reasons. 1) The fanatics among the communists believed that their system was so good for mankind, that mankind should adopt it everywhere, and if not willing to do so themselves, then it should be forced upon them. 2) The Russian communist system was a totalitarian system. To secure its power and control, it dictated the form that every institution of society should take--the politics, the family, etc., and the economy. Being a forced economy, the economy did not respond to market (willing buyer-willing seller) incentives, but to incentives passed down from big brother--the government. Thus the economic system could not produce enough wealth for its own survival. It had to survive by constantly absorbing new territories with their resources of minerals, agriculture, laborers, etc.
This is mainly because the Soviet Union (and the Russian Empire before it) had had to worry mostly about invasions from the west. This was the direction from which serious invasions came in the modern era.
The two obvious examples of invasions from that direction were the invasion by Napoleon in the early 1800s and the German invasion of World War II (1941).
Because of this, the Soviet Union wanted to be sure that it had a large buffer zone between it and its potential enemies in the west. So they thought it was very important to dominate Eastern Europe so that Eastern Europe could provide that buffer zone.