I have a green card. I lived and worked in USA for 9 mo, but now I am living the country and will reside abroad. How I can file taxes for this 9 mo? Am I eligible for EIC and child tax credit.

For EIC a U.S. citizen or resident must live in U.S. for more than 6 months in the year.
You can get child tax credit if you meet the requirements.

Also a U.S. citizen or resident must report worldwide income. Another filing requirement is Form TD F 90-22.1. Your U.S. Tax Return: U.S. Citizen or Resident with Foreign Income

MukatA has covered all the pertinent issues, but if you need professional help filing from an overseas location, email me at [email protected]. I specialize in filing such returns from an overseas location.