Someone other than Congress should be determining its pay—preferably We the People.
No this is part of the check-and-balance power of Congress. They fund the Supreme Court and the White House.
In the past they have defunded both when issues have arisen. Haven’t done it lately, but it has been done and ought to be done again.
Executive branch enforces laws. However Congress can defund it so enforcement becomes impossible. Great for when a president wants to enforce an unconstitutional law. Supremes can rule certain things unconstitutional but Congress can defund the courts in addition to passing law that prevents Supreme Court from ruling on legal issues. Supreme court members can also be removed from the bench. It has happened, and it can be done.