Your approach to this subject—the causes of the Civil War (1861–1865)—is a logical one. You could argue that the Kansas-Nebraska Act (1854) represented the last effort at compromise. Its failure meant that war was virtually inevitable. As you organize your thoughts, it is important to remember that the dispute over slavery was the cause of the Civil War. Other issues, such as states' rights, were tangential in comparison. Fugitive slave laws, the Kansas-Nebraska Act, and the Dred Scott decision (Dred Scott v. Sandford) were all about slavery.
Although the events of the 1850s marked a decisive break between North and South, the result of the Mexican War (1846–1848) was the background cause of the intensified dispute over slavery. The US acquired huge amounts of territory from defeated Mexico. Would these areas become free or slave states? The Compromise of 1850 attempted to answer this question, but it failed.
The Compromise of 1850 had included a stronger fugitive slave law. The South had frequently complained that the North was not enforcing the previous one of 1793. Enforcing these laws in the North was extremely unpopular, and the Underground Railroad helped slaves escape from slavery.
The Kansas-Nebraska Act allowed for popular sovereignty in new territories. In other words, the settlers in new territories would decide if they wanted to be a slave state or free state. In practice, it did not work well, and violence erupted in Kansas between the two groups.
Dred Scott v. Sandford (1857) was the Supreme Court's opinion on the slavery issue. Its convoluted pro-South decision in this case inflamed sectional tensions; it is widely regarded as one the worst decisions in the history of the Supreme Court.