What does the Bible say about government? Democracy? Does God want people to be ruled the same way he rules in Heaven? Does the God permit women to serve in the government?
The Bible says very little about systems of government. The nation of Israel was set up as a theocracy (a nation ruled by God or God's direct representatives), although they chose later to be a monarchy. The Egyptians, Assyrians, Babylonians, Persians, and Romans who also are mentioned were all empires, which are essentially the same as monarchies. At no point are these systems of government condemned. Democracy was practiced on a limited scale in Greece in the period between the Old Testament and New Testament, but is not mentioned in the Bible. Republicanism, which is what is really the form of government practiced in the United States and several other countries, is a more modern concept than those mentioned in the Bible. Daniel 2:21, "he removeth kings, and setteth up kings," seems to indicate that God establishes all governments, whether they agree with his system of government or not.
Probably the most complete passage that answers your question is Romans 13:1-6: "Let every soul be subject unto the higher powers. For there is no power but of God: the powers that be are ordained of God. Whosoever therefore resisteth the power, resisteth the ordinance of God: and they that resist shall receive to themselves damnation. For rulers are not a terror to good works, but to the evil. Wilt thou then not be afraid of the power? do that which is good, and thou shalt have praise of the same: For he is the minister of God to thee for good. But if thou do that which is evil, be afraid; for he beareth not the sword in vain: for he is the minister of God, a revenger to execute wrath upon him that doeth evil. Wherefore ye must needs be subject, not only for wrath, but also for conscience sake. For for this cause pay ye tribute also: for they are God's ministers, attending continually upon this very thing." This says that all governments are set up by God and we are to be subject to the government under which we find ourselves, whether it be a monarchy, a democracy, a republic, or any other form.
God would prefer that people follow Him in all things. That does not prevent them from obeying the secular government under which they live, except where those governments make individuals violate God's clear will.
Although the governments in the times in which the Bible was being written were primarily run by men, God does not prohibit women from participating. In fact, He even set up a woman, Deborah, as a judge over Israel (Judges 4 and 5). We also find women who served as rulers over Israel during the monarchy. So God, rather than prohibiting women from participation in government, authorizes it.