W2 - NY & NJ Tax

Hi,
I work for an employer with offices in NY & NJ. I am based off of their NJ office. Since I worked sometime in NY, my bonus amount in 2021 had some NY component in it that warranted a NY state W2. I am using TurboTax. Following are some hypothetical numbers for my questions below with regards to filing the returns with TurboTax

1. Federal W2 - Box 1 (Wages, Tips, other comp) - says $1,50,000
2. NY State W2 - Box 16 (State Wages, tips, etc) - says the same number as Box 1 - $150,000
3. NY State W2 - Box 17 (State Income Tax) says $3000
4. NJ State W2 - Box 16 (State Wages, tips, etc) - says the same number as Box 1 - $150,000
5. NJ State W2 - Box 17  (State Income Tax) says $5000
6. My employer emailed a word document saying that my NY taxable wage (NY portion of the bonus) - $9000

Questions -

a. In the NY Tax return, I believe I have to mention the income that is earned in NY. It will be $9000, but I only have the word document as proof. Is that sufficient ? I mean if it is not mentioned anywhere in W2, can I still report the $9000 as NY income (in the place where TT asks for the NY Income amount)

b. While doing my NJ taxes, will my state wages be $150,000 as in (4) above or will it be $150000 - $9000 (the NY portion of the bonus) = 141,000 ? If so where should I edit ?

 

c. I worked in NY for 299 of the 365 days. The % of days worked in NY comes to 81.9178% However while filling the NY State tax, it allows only 2 decimals, which is 81.92%. It throws off the actual NY portion of the bonus by a dollar or so. Is that ok ?

Thanks