Not necessarily. Article III Section 2 states that the appellate jurisdiction of Scotus is subject to “Exceptions, and under such Regulations as the Congress shall make.”
See http://www.robertwelchuniversity.org/Lectures/RWU_Curb_the_Courts.pdf
Doesn’t make sense.
The federal government is a CREATED entity, by the contract of the Constitution.
No one in his right mind would say that one party has the sole interpretation power over the contract between two parties, especially when the interpreting party is simply a creation by contract.