The Supreme Court does not have primary jurisdiction on this question (there are very few issues in which it does have primary jurisdiction).SCOTUS can do anything SCOTUS wants to do. Bush v. Gore went to SCOTUS directly without lower U.S. court review.
You are incorrect. USSC is not sovereign and can or do whatever it wants.
And bush v gore was heard at the state level and had some hearing in the 11 circuit
Yes it did, in a disastrous power grab to increase the illegitimate authority of the Federal courts even further.