As for the role of the government. The governments role is first and foremost to represent the wishes of the people, to manage the affairs of the country and enact law to keep the populace and economy safe. In the case of democratic governments, they are held accountable for their actions by the public in elections.
You talk about authority and power but it's not as simple as the government lording over its citizens. The government has power because the citizens give the government power by voting them in. I would argue that authority is always going to rest with the government, but because of the governments accountability, the power truly lies with the people.
Ultimately we decide who we trust the most to run the country and we decide who we give the authority too. If we don't like what they do, then we give that authority to someone else. You can argue that a direct democracy in which ever citizen gets a say is fairer than representative democracy, but it is also far too inefficient a system of government to run a nation the size of even may of our smallest countries. So we do the next best thing, elect the people who most closely reflect our views.