What act in essence repealed the Missouri Compromise by allowing popular sovereignty in territories that had been legally closed to slavery?
The Dred Scott decision repealed the Missouri Compromise because it was said to deny a man's right to property and that it is unconstitutional. The decision legalized slavery everywhere, and the Missouri Compromise said that there equal free states and slave states, and so now all states are slave states.
What Stated that Kansas and Nebraska would be admitted to the Union on the basis of popular sovereignty?
The Missouri Compromise of 1820 admitted Missouri as a slave state, and Maine as a free state, to keep the balance of slave/non-slave states equal in Congress. It also established the 36-30 line, and said that slavery would not be allowed above that line except for in Missouri. The Compromise of 1850 admitted California as a free state, and gave the South stricter Fugitive Slave Laws as a way to "balance" the deal. It also…
Did the Kansas-Nebraska Act temporarily suspend the Missouri Compromise until the Kansas territory could determine the status of slavery?
No. The effect of the Kansas-Nebraska Act (1854) was to supersede (nullify) the Missouri Compromise, rendering it inapplicable to future states. The geographical division was not applied, but rather "popular sovereignty" within a state would decide the issue of slavery there. This resulted in internecine warfare in the states of Kansas and Missouri, and murderous attacks by both sides (abolitionists and pro-slavery). The Missouri Compromise (1820) was never actually repealed per se.
The Missouri Compromise had stated that all states above the 36 30 parallel would be free, and all below it would be slave states. This had established a begrudging peace between the North and the South, which lasted until the Kansas Nebraska Act of 1854, which repealed the compromise and introduced the concept of popular sovereignty in determining whether a state would be slave or free.