I have lived in the U.S. for more than 5 calendar years. I can be treated as a resident alien for tax purpose. My qualified child lived with me for the whole year. I used Turbo tax software and it said that I could claim EIC and child tax credit. But I am not sure because my truly legal status is F1 student neither a citizen nor a permanent resident.
You could qualify, but there are a few factors. If you are married and you're spouse is not living within the United States or does not have a Social Security Number, you must disclose this fact. You will still be allowed to claim Child Tax Credit, but not EIC, if your child lived with you for more than 6 months and has a Social Security Number. Since you have been on F1 for more than 5 years, you are considered a US resident for tax purposes.
You could qualify, but there are a few factors. If you are married and you're spouse is not living within the United States or does not have a Social Security Number, you must disclose this fact. You will still be allowed to claim Child Tax Credit, but not EIC, if your child lived with you for more than 6 months and has a Social Security Number. Since you have been on F1 for more than 5 years, you are considered a US resident for tax purposes.
We are legally separated. He has SSN but I do not have his SSN. But he lived in the U.S. He is not a citizen or green card holder. Can I claim the EIC?
If you have a legal separation, yes. You may claim Head of Household, and you will qualify to claim EIC if your income allows you to (which it sounds like it does).