Correlation does not equal causation in this case. There is a third omitted variable which likely causes both poor academic performance and poverty.
Bearing in mind at lower income groups the difference between Asian and White/Black/Hispanic kids is greater than at higher incomes.
Yes, but when you mix students, the poor and minority students are not isolated and instead are exposed to greater educational opportunities. It is unfortunate that this tends to express itself in racial terms because it makes it difficult to articulate. However, a black student at a racially mixed school, with otherwise identical spending, attention, etc., will on average achieve much higher than a black student a predominantly black school, due primarily to exposure to other students from backgrounds valuing education. (This wouldn't apply to a black student with highly educated parents/parents who value education, obviously, but sadly that is not the norm.)