First, every court of appeal can strike down a law as unconstitutional. The Supreme Court is only special in that there is no further appeal.
Second, case law absolutely determines the interpretation of each text, and each court is mildly bound by its own precendent (via stare decisis), and completely bound by the precedent of superior courts.
Third, there is no tension between these facts and people being judged individually and being equal before the law. The law must (in principle) be applied equally to everyone.
Any federal court, not just the courts of appeal.
You can be charged with a crime if you knowingly, falsely yell "fire!" in a crowded theater and someone gets hurt as a result.
The case you linked is not actually a ruling on whether you can do this.
In reality, the phrase was an analogy used to justify the conviction of a man who committed the heinous crime of… making and distributing leaflets opposing the draft in World War I. So for all the high minded rhetoric in the First Amendment, it may not provide all that much protection if your speech inconveniences the government sufficiently.
One might also be tempted to draw inferences from the fact that Schenk, the man whose speech was considered not worth protecting, was a socialist pacifist, while Brandenburg, whose free speech was considered more worthy of protection, was a KKK leader promoting violence against Blacks and Jews. In the US, protecting the civil rights of Nazis has become a litmus test of civic virtue across the political spectrum. Unfortunately, that protection is extended far less vigorously and consistently to other political views.
https://en.wikipedia.org/wiki/Schenck_v._United_States
https://en.wikipedia.org/wiki/Brandenburg_v._Ohio
https://en.wikipedia.org/wiki/National_Socialist_Party_of_Am...
Yelling "fire" in a crowded theater, for example [0]. Another comment in this thread talks about the "clear and present danger" doctrine that came from the case. That case was followed by the Brandenburg v. Ohio [2] case in 1969, which instituted the current methodology used for determining what is "allowed" speech. That rule/methodology is called the "imminent lawless action" rule.
[0] https://supreme.justia.com/cases/federal/us/249/47/
[1] https://en.wikipedia.org/wiki/Shouting_fire_in_a_crowded_the...
[2] https://supreme.justia.com/cases/federal/us/395/444/