There are not many, if any, I grant you but it's not because of the Constitution more a case of politics. Trials can be moved more easily to other counties but I would submit that the media destroyed any hope of a fair trial and it should have been moved to the Supreme Court.
No. It's because the Constitution that it can't move to another state. Federal supremacy says that it must move to the federal system instead of moving to another state.
Chauvin plead guilty to his federal charges and avoided a trial.
The Supreme court does not conduct trials. It can't conduct trials since it is not a finder of fact.