Resident alien or dual-status alien?
I am from Hungary. I have been working in the USA from 01/11/2010 until 08/31/2012 as a J-1 research scholar. I was absent from the USA 11 days in 2010, and 15 days in 2011. In 2012, I was present in the USA from 01/01/2012 until 09/11/2012 continuously. After that we permanently moved back to Hungary.
For tax year 2012, I received forms 1042-S and W-2 from my employer. On 1042-S there was no tax withholding reported (because of a tax treaty exemption), and on W-2 there is a roughly $3000 withholding.
My wife was with me for the whole time as a J-2 dependent. She did not work in the USA, and she does not have a SSN or ITIN. We had two children who were born in the USA in 2010 and 2012, and they both have SSNs.
My questions are:
1. Do I need to file my tax report as a resident alien or as a dual-status alien?
2. If resident alien is the answer to Q1, how can I report the income on my 1042-S on form 1040?
3. Together with my wife, can we file the tax report as "married, filing jointly"?
4. Are we eligible to deductions and credits after our two children?