It means NYC must do this three times more to get to herd immunity, and strike the right balance each time. Still it is far from safe since people can come from the rest of the country so it’s not a real herd immunity.

Your comment implies that "do[ing] this three times more" would be very difficult. That's totally incorrect. As the level of immunity rises, R0 goes down naturally. The effect is huge at even 20%. Giant at 50%, etc., especially with moderate social distancing. Moreover, there is every reason to believe that some people are just naturally resistant/immune to the virus. I believe Bergamo never got above 57% sero-positivity and even the USS Rosevelt was around 60% sero-positivity. It seems impossible to believe the other 40% weren't exposed. If (okay a big BIG if) 40% just don't ever get COVID, and 50% get it but have mild moderate symptoms (the data strongly supports this), NYC is basically done with this emergency.

Will they be immune in one year? Two?

The data on long-term immunity for COVID is non-existent, that is why the experts are being cautious. However, the data on animal coronavirus vaccines (not COVID) is very suggestive that yes they will be immune in a year and two. Coronaviruses do mutate but do not mutate like the flu virus does.