Yes. Please see the information in this LINK.
Yes, each year is independent so the amount of time one spent in NYC in a prior year is irrelevant to the current year. The 183 day rule only applies if you were not domiciled in NYC, meaning that you also had a home in another state for more than 183 days.
Not paying taxes if you are a resident less than 183 days a year in NYC applies to stock income like capital gains, dividends or money earned in other states. All money earned in NYS and NYC from a job is taxed by NYS and NYC even if you don't live here at all and commute everyday from other states. And your home state will also tax your NY earnings if the state has a tax since it is your home. Though when you file a tax return in your home state you may get a tax credit for the taxes you paid in NY.
If you live in NY less than 183 days then what you made in another state where you live/lived is not taxed in NY.
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