What type of government was presented in the novel and what type of contact did people have with it? How did the government help shape society?

One can infer that the type of government is some form of totalitarianism. It is one in which the people seem to have little contact and no control. It's purpose, besides sustaining itself, seems to be to try to make people happy so they will not question or even need to meet with government officials. However, Bradbury purposely leaves out many specifics about the government in order for it to seem more monolithic and mysterious. This adds to Montag's sense of frustration and helplessness because he cannot find the answers he seeks. The only contact he seems to have with any kind of authority is through Beatty. Thus, society is shaped through the media and the media substitute for any real human contact, with the government or anyone else. As long as people are entertained, the government seems to believe, they will be subservient and easily manipulated. If not, there is always the mechanical hound, another symbol for lack of significant contact, to seek out and destroy any protest. Ironically, this lack of contact backfires with Montag, and apparently others, or there would have been no need for the mechanical hound or for the "book covers" to exist. Luckily, the government does not seem that effective in dealing with foreign policy and seems to ignore a real problem that leads to its own destruction.