But isn't that the question - what is a god? Anyone with enough power, charisma, followers can run around announcing they're a god. Some people may believe them. Look at Corypheus. You play the entire game saying he's not but people really did believe he was. Look at the Inquisitor. The "Blessed Herald of Andraste". I spent the entire game playing "Life of Brian" because I knew I wasn't. I was just a person who was in the right place at the wrong time. But people still believed I was their freaking Messiah. The Warden's story is legendary. In time their feats will become even more ludicrous as history forgets the truth. Same thing with the Champion. People already probably view them as demigods.
That's also the whole point of faith. Or at least what the game tries to teach you. If you believe in something hard enough, is it true? Does it matter? In the end all that matters are the actions and choices you make as a person.
Morrigan during the Well of Sorrows mission says something like "what is a god if not a creature of immense (please correct me if it's not exactly the word she uses, mined to find this dialoge on yt and google and couldn't find the exact transcription) power?"
For me it's.... it's exactly what gods in DA lore are. The way if you're born/made/created with this power or actually you claim it is a secondary issue.
I totally agree with all your points. Since the DA:O all your achievements that everyone praises you for, are just a sum of coincidences, some of your skills, your actions and how people chose to think of you, but it's you who you chose to be.
The whole construction of all DA games though forces our heroes to become somehow special, demigods, as you say. Warden unifies Ferelden, deals with impossible, Champion protects the city, Quizzy has the fancy green glowing hand etc. All DA heroes are being pushed for more, they reach where the others don't. This is why I believe the whole lore is leading to a choice: if you would have the possibility to have even more power, to become a "god" = creature of unmatched power, will you chose to reach for it?
Although my BW lore predictions never happen (never expected the ME3 ending
)