Exactly. I think there is again a subtle difference between classical and medieval latin. For Romans the meaning was indeed related to Gods, but they didn't take it in the strict religious way (then 'dutiful' is more accurate). On the other hand in medieval scripts pius means definitely 'pious'. Piety as a virtue morphed as well as the meaning of the word.
You raise good points, donfrolimo. The noun pietas and the adj pius evoke several Roman virtues including loyalty, devotion, and a sense of duty. "Dutiful" for the adj in the Roman period is a good gloss. As CollinParry noted, it's THE epithet for Aeneus. It means he is dutiful to the obligations to his family, to his people the Romans, and the divinities (hence he leaves Dido behind).
From duty. A dutiful son: a son that is respectful for his parents, loving, obedient, accomplishing his filial duty.
A dutiful soldier respects and honours his fatherland.
Someone who respects and honours an authority, is dutiful toward it.
Very similar to the Latin "pius", except maybe the Latin could also mean honouring the God(s), and I think it would be more "pious" in English.
Latin word order is very flexible, so there is no hard and fast rule for this. However, you are correct that adjectives typically* follow the noun, unless the intent is to emphasize the adjective.
*There are some adjectives that are more commonly placed first. Numeral adjectives, adjectives of quantity, adjectives of size, demonstrative, relative, and interrogative pronouns and adverbs, tend to precede the word or words to which they belong. (from section b of: http://www.perseus.tufts.edu/hopper/text?doc=AG+598 and also from http://rharriso.sites.truman.edu/latin-language/latin-word-order/)
So, quinque mariti (5 husbands), or parvus puer (the small boy), but most of the rest will come second unless intentionally emphasized (and one could argue that the preceding examples are the way they are because these adjectives are typically added for emphasis anyways).