IRC125

Assuming you are posting the boxes from your W-2.

Since there is a difference of 2,000 from Box 1 and Box 3, I would assume that the pension (IRC414H) was before tax. 

This would make sense since these funds would not be subject to Federal tax, but would be for state tax. That amount is not included in box 1. 

That 2,000 would be an addition to your New York State income. 

If you also contributed to a flexible savings plan, (IRC125) I would assume this was done with after taxed dollars since there is only the 2,000 difference between box 1 and box 3 and box 14 is showing 2,000 to a pension plan. 

1. No, the 1,000 flexible account does not seem to have been deferred. The difference is whether the amount would be an addition to your New York taxable Income. If it wasn't deferred, it is included in Box 1 and does not need to be added back in. You should check with your company's payroll department. 

2. No. Box 14 on a W-2 is not used by any tax software. It is used by your company's payroll department. The answers I have given are educated guesses based on the information you provided, but box 14 can be used for almost anything. TurboTax cannot make tax decisions on information from box 14 on any W-2.