I do not live in NY. Is my "federal income that was derived from New York sources" the total amount of wages I earned from the company in NY?

It depends.  What determines whether or not your income is taxable in New York depends on whether it is New York Source income.  There are two types of income that New York considers to be New York Source:

• Wages Earned In New York State.  This is fairly simple:  you are working within New York State borders, so New York has the right to tax you for the income you are earning inside of New York.

• Telecommuting for a New York Company conducting business in New York State.  New York argues that telecommuting (working from home) is for the benefit of the employee, so the income is being produced in New York and is therefore taxable to New York.  If you telecommute, and your employer has established with the state that your work is for the employer's convenience, then your telecommuting income is not taxed in New York.

Otherwise, the fact that you work for a New York company does not in and of itself make your income taxable in New York.  You must be working in New York for it to be New York income.

It depends.

Per DanielV01's response above, it will depend upon if it's considered New York source income. 

You can also look at boxes 14-15 on your W-2 Form, and if you see NY as the state in any of these boxes, you usually have to enter information in the New York state section in TurboTax. 

This will ensure you get a refund for any withholdings that you potentially did not have to make if you determine you did not have any New York source income.

Filing requirements for nonresidents of New York

@Dapoli

Reread Daniel's answer. What sort of income do you have that is not covered by the first or second bullet point?

@rg1004