No, DA is how well the pages on the website may rank. It is domain specific. PA is how well the individual page may rank, irregardless of DA. We all know that pages on a more trusted site have a better chance of ranking higher for more competitive terms.
Your first example is correct. You could have a PA of 60 and a DA of 10 on a site.
I don't think I agree with your second one though. Page metrics are still better correlated with rankings than domain metrics. It would be better to have a link on a high PA page than a high DA domain, though sites with a higher DA will often have more pages with higher DA.
But with your two, I would say that a DA70/PA30 is better than a DA35/PA40, because a PA30 is not too much less than a PA40, but that DA is powerful.