I think the Archdemons are actually Demon-possessed High Dragons. We are talking extremely powerful Demons by the way, quite possibly Greater Pride Demons or something more. Also too strong for normal hosts, hence the need for Dragon bodies, as Thedosian minds can snap. We know Demons often teach Blood Magic to Magi in exchange for physical forms. We also know that Blood Magi can force unwilling or unsuitable hosts to accept a Demon. From here there are two possibilities for their creation:
First, they could simply have possessed High Dragons of their own accord.
Second, they could have offered the Magi Blood Magic in exchange for their Draconic forms.
As unlikely the second option is, lore-wise, I think the possibility should remain open. For the rest of the argument, where applicable, I will assume the first option is true.
The Archdemons were once the Old Gods, but apparently they were imprisoned underground. If anyone remembers the Primeval Thaig, the Red Lyrium Idol may have been made in worship of them. Hell, the idol may have let them in at that. We know Dragons show up underground too. Assuming the Dwarves used to worship the Old Gods, the idol would have let them in by tearing the Veil. They would have taken over the most powerful bodies they could, like the High Dragons. Then they would have rampaged wherever they could and then the Ancient Dwarves who did not serve trapped them. This would be the "imprisoned beneath the earth" part, and then the dragons slept, the demons within trapped as well.
And when they slept, they dreamed.
The Fade would have allowed them to communicate with one another and with the people of Thedas. Cue the Magisters, who the Archdemons taught powerful Blood Magic to. Once the Magisters had enough power, the Archdemons told them of the Black City, and spoke of great power within. Greedy and proud, the Magisters entered the Black City, and came back as Darkspawn. Then they would seek out their masters and wake them from slumber.
So far, some of you will be wondering where the Taint comes in, and why the Black City was important. So let me ask you; where would seven or so ancient, EXTREMELY POWERFUL Demons, come from?
Does an ever-present city lurking at the edge of every dreaming mind sound right?
Maybe the idea that the more territory it has, the more powerful the demon gets, has crossed your mind?
Perhaps you just realised that the one unchanging thing present in every other domain may well be a domain itself?
So did I. The Black City is present everywhere in the Fade, so the Demons that inhabit it must be frightening indeed. No other Demon has tried to enter it as far as we know, so maybe they are afraid of what lurks within. The Black City would be where they are strongest, strong enough to twist the invading Magisters into monsters. Monsters that would spread their new curse in the physical world, causing the Darkspawn to exist. We know for a fact that demons can alter the Fade however they wish, so altering the bodies of Magisters who physically entered the Fade would be every bit as simple.
The Taint is like the Red Lyrium Idol. They both have a nigh-irresistible "song" or "call" that the right people can hear. The Red Lyrium could call to Dwarves, and probably others as well given enough exposure. But that would bring guests. Guests who heard the song and knew what it meant. Grey Wardens of advanced age can hear the Call as well, and they are the enemy. The Dwarves who sealed the Archdemons may have found them through the Idol's Song, but the Taint is silent to outsiders. The Taint also acts as a direct channel between Darkspawn, allowing a hive-mind to exist. These connections could conceivably allow Demons to body-jump before they are destroyed, and soulless Darkspawn are good hosts.
On the topic of Flemeth and this belief that she is an Archdemon; I don't think Flemeth of all people is an Archdemon. But I do think we have seen someone like her before. Remember a certain other body-snatching piece of once-human filth? Magisters seem to like their immortality. I think Flemeth was actually one of the Magisters that attempted to invade the Black City, and she managed to escape her tainted body. Corphyeus was implied to have stolen the body of Janeka/Larius before he kicked the bucket, and Flemeth pulls body-snatching too. Flemeth probably needs the ritual magic to force a transition between non-Tainted bodies, as they aren't made for it, while tainted bodies benefit from the hive-mind connection. She would also be after the "power" she was promised, and maybe hoped that possessing a purified Archdemon child would give her that. But the Taint is something she would obviously want to live without, so that the Archdemons can't possess or control her. As for the age thing, Darkspawn don't really need to eat due to the taint sustaining them, so it's no great stretch to think that they might not age. Corphyeus may never die until he is killed, but Flemeth occupies a mortal body. Still aging and all, so yeah.
I could be entirely wrong, but there's my two cents.