1) I am mixed race (no hyphen) is a common phrase for people with multi-ethnic or multicultural origins.
2) There are different ways to say this, but if it's 50-50 then it's better to say, "I am half-Chinese and half-American."
"Half" is better because it shows the division of your multicultural makeup. For example, I can say I am half-Brazilian and half-American even though those are two cultures and not really ethnicities. Even if we talk about blood or ethnicity, using half is still the most popular form I hear.