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Does Google treat the two as two separate domains for all intents and purposes?
Yes but depending on what you have in mind. If you have a subdomain redwidgets.domain.com and it focuses on red widgets, while domain.com and www.domain.com are the corporate pages, are you asking if both sites will display in the same serp, e.g. the company name? Appears to be Yes.
Yes, different PR for subdomain.domain.com in my experience. Good examples to check are the multinationals that use the country subdomain, e.g. au.yahoo.com has less toolbar PR than www.yahoo etc.