I want to express the meaning that I look like a typical East Asian. Can I say that:
1) I have a (typical) Asian (physical) appearance?
2) I have an Asian look?
3) I have an Asian face?
Or any alternatives to introducing one's ethnicity?
Your "appearance" could include the way you dress, not specifically your face.
Leaving aside any thoughts on whether it is okay to say "Asian" (as I believe some people find it a little non-specific and therefore a generalisation) I would suggest saying:
I have typically Asian features.
What you are looking for is countenance, which means "the appearance or expression of someone's face."
You can say, "I am of Asian countenance."