As to NYC deaths, many people currently infected will die in the future. You can make various estimates to account for this but a reasonable first approximation is to double current deaths based on NYC’s infection curve vs South Korea’s.
>"The overall case fatality rate as of 16 July 2009 (10 weeks after the first international alert) with pandemic H1N1 influenza varied from 0.1% to 5.1% depending on the country."
Whenever I have gone or brought my kids when sick, they perform the test to rule out any potential need for antibiotics. When I asked, they said it's systematically reported to the the CDC as part of their flu surveillance system, whether positive or negative. That surveillance network is significantly more robust than a survey.
(Sorry, couldn't resist).