They are, and California voters passed a ballot initiative limiting the rate property taxes can increase. End result: nominal tax rate above of 1 percent, effective rate at around half that.
Only in America. And not even in all states. But certainly in California!
Not exactly. Thanks to Prop 13 and Serrano v. Priest most school funding is from the state in California, and allocated pretty equally across schools. Parental donations are what give some areas better resources.
Note that some states do have re-distribution schemes, such as NJ (Abbott Districts).