Regarding 1, even after whites-only schools became illegal, little changed. Previously legally whites-only schools stayed in-practice whites-only, often with explicit discrimination by racist parents and teachers to discourage any black people from sending or keeping their children in the school, but other times simply as by-product of housing inequality. It was hard for people in a black neighborhood - itself created by now-defunct discriminatory laws that had huge long-term impact - to send their children to a school in a farther away white neighborhood.

The fix was to forcibly integrate schools: explicitly mandate not just that black students be allowed, but actually that they are integrated in significant numbers, including by providing special facilities (school buses) to take them to the better schools that were farther away from their homes - the policy known as "busing" [0]; a form of (positive) discrimination.

Of course, as the article notes, this can also have negative consequences, so any such measure is far from easy to apply.

[0] https://en.wikipedia.org/wiki/Desegregation_busing