I think you have more questions about the Bible than about how Christians feel about it. You clearly need to do some Bible study, though, because there is a very large number of verses that can address homosexuality, from various perspectives. For example, The Bible is very clear on what marriage is according to God. Marriage is between one man and one woman. (Clearest in the NT) It is clear that sex outside of marriage is sin. Therefore, when a person has sex outside of marriage, they are in sin. This would clearly mean that since gay marriage is not God's plan, it is outside of marriage, according to God. Thus it is sin.
One must study the Bible in more ways than just topical. one has to look at various angles of an issue.
There is not a difference in the God of the OT and of the NT. Because of what God was doing in the OT, establishing a kingdom, and designing the boundaries, He worked in some really radical ways. In the NT, The kingdom was established by definition, and design, and Jesus was the King of that Kingdom. God began to work in a different way. However, God did not change in character. In the NT God became more personal with the people of the Kingdom, because He designed the Kingdom as a body who has a real and personal relationship with Him through the Holy Spirit.
The OT was elementary school, and now we are in high school. We can take in more, but, by design, the reason we can is because the Holy Spirit enables us to do so. God gave the laws of the OT to show mankind that they were not able to abide by a righteous standard. We would violate His laws. Once He established that, He made a way, because of His awesome love, to be forgiven. He showed that all through the OT, but in the NT He gave the true Lamb for the eternal, once needed sacrifice for all who will accept it.
The OT is as significant as the NT. One must learn to walk before they can learn to run. In the NT it is like this, as babies in Christ we need the milk of the word, but when we mature it is the meat that will be our strength. The OT is the milk, and the NT is the meat.