2. SCOTUS has the power to hear controversies both between states and between citizens of different states. It also has the power to hear controversies between a state and a citizen of another state.
3. There were two main holdings in that case: One, that the due-process clause could be used to strike down actual laws (in this case the antislavery law in the territories), rather than methods of enforcing those laws. This illegitimate concept is what's known as "substantive due process", and it's been the germ of a whole field of judicial activism, including Roe vs Wade. The other holding was that black people couldn't be citizens, and there was no constitutional justification for that view.
1)Are you saying that Dred Scott was the first time 5th amendment due process was used to strike down an act of congress?
2) What was the reason that the court gave for deciding that the law in question violated due process?