Yet another case that shows why the death penalty is such a bad idea

[Pindar]

a) If it is not the government's job to look after people, what right do they have to govern peoples lives at all?

Government has no right to govern people's lives. Government exists at the behest of the governed: its terms and conditions are determined by the same. Government is a construct.

b)What moral force does the government have in getting involved in peoples lives if not for looking out for the people?

The essential justification for government from the Enlightenment forward has been protection. This means protection against the predatory practice of other groups (polities), and internal threats (criminals). To use Hobbes phrase, life in the absence of government would be: "nasty, brutish and short". One may consider this rationale a moral force, but it is more akin to a simple expediency. Arguing a moral basis for government involvement is problematic from a secular perspective.

c) What would you think of a socialistic system that was geared to create individuals who are independent and engaged in society?

A collectivist system geared to create individuals...hmmm.

Despite the stickiness of the above, I do think I have an idea of what you are aiming for. The founders of the American Revolution were deeply concerned with justifying a move toward democracy. Recall, democracy was not a new idea, but it was a rejected idea. Most saw democracy as mobocracy: the unruly masses lack the wherewithal for self governance. The Founders argued that freedom could be justified to the degree that freedom was used to instill the necessary virtue to govern society: freedom for freedom's sake was an absurdity. Notions of the good and the individuals essential role were paramount concerns. The good and its attendant virtues appealed to the Judeo-Christian Tradition. This is one of the reasons they made reference to natural law with language like: unalienable rights. From this perspective government does not create morality, indeed cannot create morality, rather it creates the space through which moral agents arise. A simple example of this was Jefferson's Anti-Federalism. This agrarian model saw that the development of the moral man required independence from government bureaucracy and dependency. The citizen who can properly guide the state cannot be a slave to it. This is one of the reasons Jefferson was so keen on the Louisiana Purchase as it would provide the space where men could live and develop free of government intrusion: corruption and sycophancy.

Socialist models as they are typically put forward with their command economies and collectivist mentality are an assault on the very basis of the moral which begins with the subject, the "I".