This is one of those places/cultural activities that NY is out of sync with the rest of US, and (other parts of the world)
In most of US, (Oz, too?), getting a car, and learning to drive is a right of passage.. most kids get a licence age 16 and have a car, before 18.
In NY State, you can get a licence age 17, and in NYC you can't get a licence till 18! and most NYC kids don't learn to drive in HS. Many learn in the summer before they go to college. Some, like my son, never really learn to drive.. he live in CA, and does have a licence, but he bikes to work.
half the people i work with (7 out of 15) don't own cars.. 5 of the 7 don't even know how to drive. it is real common, for adults not to need to drive or even to know how to drive in NYC. This is normal in NYC!
Doing Donuts, or Circles or Cookies? unheard of! NYC kids take buses and subways, and to be daring, learn to jump turnstiles--or worse!
as for messing up a teachers yard? there are over 1 million kids in NYC schools (elementary/middle/high), and teachers? i forget-- but they come from all over NY area! Teachers might live in Bronx, and teach in Manhattan, or vis a versa-- it really unlikely a kid would know a teacher out side of school.
(that is something isn't it? NY has more kids in schools that most US Cities have as a total population!)