1. What is the red zone?

The correct answer is: " he knew this was an extremely important case".

The questions refers to Brown v. Board of Education, which was a case that led to the enactment of a landmark decision by the US Supreme Court in 1954.  

The case was about the constitutionality of the "separate but equal" principle that was accepted in a former decision enacted by the US Supreme Court in 1896 in the Plessy v. Ferguson case. Such decision allowed the proliferation of segregated schools under the belief that, if facilities were equal in quality, such education system was not violating the equality of rights provision that had been guaranteed for all US citizens by the Reconstruction Amendments to the US Constitution.  

Brown v. Board of Education overturned the abovementioned previous Supreme Court decision and declared segregation unconstitutional, claming that, in practice, it actually deprived black students. The court published a deadline and all public schools nationwide had to abolish such practice and to adopt racial integration.