The schools in the wealthier areas get no more funding per student than the ones in the poorer areas as far as I can tell. The state provides much of the funding with local property taxes making up most of the rest (federal money is a small percentage). Those tax rates are the same across the city and I am not aware that the money paid by a property owner in one part of the city is allocated specifically to their local school instead of the whole district. Incidentally despite having much higher funding than the average schools in surrounding states New Mexico has long been near the bottom of the list for school performance nation-wide. Usually trading places with Washington D.C. and Mississippi.
This depends. A brief foray in the internet suggests that Albuquerque may actually do this. However, where I live, there are 2 different funding formulas. The state funded, and the property tax funded. If your property tax income is high enough, you become "basic aid", meaning - the district keeps a certain % of property taxes for schools. If it is not, then the state "makes up the difference", and the district funding is per student.
Our district is funded per student. Approximately $8000/ year. The one next door is basic aid. Where Oprah lives. $22,000 a year.
Regardless, you are missing the big thing: parental donations. The "highest ranked" (wealthiest) elementary school in our district raises $600,000 a year in PTA donations. That can pay for a whole lot of extra. The lowest ranked may make a few hundred selling popcorn.
However, those children in private schools are more likely to have parents who have college degrees or advanced degrees, two-parent households, wealthier households, etc. Basically all of the characteristics that are correlated with higher student achievement - regardless of race. Would eliminating those private schools and enrolling all of those kids in public schools increase the education of their poor classmates with a single parent who has a high-school education or less? Or would those same students perform better regardless of the setting because they have a stable home life with parents that are more likely to value education (as evidenced by their own educational attainment)?
On this one, here's the thing. I pulled up data from 10 randomly selected elementary schools in Albuquerque.
The two ranked a 10 had a percentage of students living in poverty: 9%, 21%
The two at an 8: 38%, 60%
The two at 6: 57%, 100%
The four at 2 an 4: 100%
Poverty of families is a STRONG correlation (the strongest, really). Where schools have a smaller % of students in poverty - they get two advantages. More money from donations for extras, and fewer students who need additional intervention.
For fun I found the PTA budget for one of the #10 schools. $130,000 a year, $30,000 of that for a STEM teacher. Because STEM is extra, and the poor kids don't get it.
Would it help if private school parents put their kids in public schools? In a word, yes. Multiple studies have shown that having having higher achievers in classes brings up the whole class. Plus, those private school dollars get donated to the PTA.