No it doesn't. Your Christianity teaches that. I've been in churches where they have flat out said this stuff is less about truth and fact and more about the meaning of the story being told. When you have idiots who believe it is literal and not a tool written by man as an interpretation of the word of God you have problems in this country. People are free to believe what they wish, when those beliefs interfere with others lives like hatred of homosexuals or other religions then it's an issue that needs to be addressed for the greater good of ALL people, not just those with 'Christian' beliefs.
Yes it does. I'm not sure what churches you're talking about, but don't confuse how some churches interpret the Bible with whether Christianity teaches that the Bible is God's literal word. Christians have been teaching that the Bible is God's literal word since this country's inception.
Christianity doesn't teach hatred of homosexuals. It teaches to hate the sin and love the sinner. Some Christians lose sight of this teaching, but that represents a problem with some people, not with Christianity.
People who happen to be Christian have every right to use the democratic process. If you or anyone disagrees with them, then go vote.