How should someone who writes and records an album verify that the songs he wrote don't accidentally infringe a third party's copyright?
Release the album. If you get sued for copyright infringement and lose the court case, you have committed copyright infringement.
Did you miss the part where the President appoints the justices, and the people elect the President by simple majority?
False: https://en.wikipedia.org/wiki/Electoral_college (did you ever take Civics?)
The only way the President goes against the justices is when the people have a change of opinion and elect a President that totally disagrees with the sitting justices (who were appointed before he took office).
Like when Republican John Roberts struck down the mandate in Democrat's Obama's Affordable Health Care Act? Also, there are ways around a stacked Supreme Court: https://en.wikipedia.org/wiki/Judiciary_Reorganization_Bill_of_1937
It's not like there's some worldwide authority on what's acceptable to teach in schools; that's up to various levels of government (depending on the country). If a country decides to teach Creationism as science, there's nothing that's going to stop them.
How about the Supreme Court? https://en.wikipedia.org/wiki/Edwards_v._Aguillard
We have a equal opportunity Calculus class -- it's fully integrated.