Can non Americans work as doctors in America, in one of the big hospitals?

The short answer is yes. Though they would be required to have a Green card to work in the US (and I'm assuming you meant the US by America) as well as a doctor's license to be employed by a legit US hospital.

Yes, over in Cali half of the doctors are immigrants.

Not from mexico, but instead China, India, and Russia.

~Aizen

Yes.

Yes, but only if they're certified to practice medicine in the USA

Yes.

Seriously?

Only if they aren't you.