Discriminating someone because of their Chinese ethnicity would be hard to justify but what about Chinese citizenship (especially if it's the only one) or ties to China like family living there? Those would make someone vulnerable to pressure by the Chinese government.
No. As long as someone has a green card or citizenship, who cares where their family lives? The only exception would be for national security clearances, and those affect Americans as well.
Is it legal for a private US company to apply (some of) the same tests used to determine national security clearances in its hiring decisions? Or is the government the only entity allowed to make decisions that way? I'm genuinely asking, I haven't thought about this conflict before.