True for public schools.
2) Funding often comes directly from the local school district, most of which are already severely cash-strapped. The problem here is that the cost of a single student attending a school district is largely buried in fixed costs: when the state takes $6000/yr from a district and gives it to a charter school, the district's costs do not decrease by $6000. This makes school districts worse, which accelerates flight to charter / private schools.
Open enrollment causes the same issues.
3) Educational standards are different -- Also, most states offer some sort of funding incentive based on test scores -- which just encourages schools to play the numbers game by finding reasons to suspend/expel struggling students, encourage cheating on tests, etc.
True for public schools.
Public shools in NY are zoned so if you want your kid to go to that good school in Tribecca you most probably have to move there.