This might be worth crossposting to /r/AskScience for their input on the genetics side of things.

Also, as another question, based on the depictions of native Americans I've seen, it seems like facial hair was very rare. Is there any historical explanation or information behind that?

Here is a recent post on the facial hair question. I can't help you with the baldness question.

Male pattern baldness is in fact virtually unknown among native americans - here's a magazine article which mentions the fact, but it doesn't give a source: http://health.ninemsn.com.au/menshealth/grooming/695086/the-bald-truth