That's part of what makes it confusing. Morrigan says "The child will bear the taint and the Old God's soul will be drawn to it like a beacon".
The Archdemon soul is bound to the taint which means that every time the dragon is killed it's soul is attracted by the taint of others contaminated beings and cannot go into the fade,
which seems to imply that the "darkness" of the taint is somehow akin to gravity for the soul who seem to be in itself tainted.
I argued once that the implications of this may be nefarious for all the Grey wardens if it is something non Old god specific because it means that the taint don't alter only the body and the blood but the very soul of whoever is infected by it.
As for the "beacon" i think it means that the ritual is altering this signal to be more specific in the unborn child so that the old god soul would not missed it.
Actually what is difficult to explain through logic is not the concept in itself but how that is possible.
I see it as a form of lore
contradiction or of Morrigan hiding informations.
In theory the Dark ritual as it is presented shouldn't work.
If the child bear the taint and at that stage has no will of its own then it means that the archdemon should reborn once again from Morrigan (rather than the soul being purified to its former self)unless she is using the GW resistance to not make it happen, which means she is hiding others details of the spell.
What is truly complicated to explain is why the child is more of a "beacon" than the darkspawns or the Warden who perform the final blow which is the closest being to the soul.
I think there are only two theories:
1) Morrigan is using blood magic to enhance the taint within the child and she is hiding details of what kind of blood magic is and how it operate
(I imagine with her life force or the one of the child)
-This however does not explain why the Archdemon don't reborn inside her since even if i'm aware that blood magic was shown to be able to cleanse the taint (at least for eluvians) here it is used to call in combination with the taint an archdemon soul which means that the child is tainted when the soul reach him;yes it is Grey warden taint with resistance however this means nothing because it did not helped The Architect when he failed,since the soul of the old god was tainted by GW blood and became an Archdemon because of it.
2)Morrigan need a Grey warden not only to perform the ritual but also to kill the Archdemon.
The Grey warden is used to absorb and filter the soul of the archdemon and give to it some resistance, then this altered soul has no other choice but to seek the child because it was filtered and is more in tune with the child rather than the darkspawn thus it seek only the child.
The filtered archdemon soul is completly purified when it reach the child.
-This theory has its issues as well since it does not explain
if it is actually possible to dodge soul annihilation when the Archdemon soul enter into a Gw but come to think of it we don't know the time frame of the Ultimate sacrifice.
Most importantly it does not fully explain how the old god soul is restored which is the very issue of the dark ritual.
Except that the whole reason the Grey Warden process works is because two Souls cannot share one body.
I'd assumed that Kieran wouldn't have any other soul, since this ritual was designed to get around a problem caused when there were two souls in one body.
1.My impression is that Urthemiel left him enough control of his own mind and body to develop normally, and mostly only manifested as a voice in Kieran's head that told him stuff he wouldn't otherwise know
2.Surprisingly enough Urthemiel was a fairly pleasant "roommate" who shared the body with Kieran peacefully.
I think the player was pretty much misinformed by the narrative in DAO.
My own conclusion is that the ritual was designed to dodge the issue of different wills into one being not of multiple souls into one body.
If an Archdemon can reborn within darkspawns is more likely because their will is already subjugated rather than them lacking a soul.
Flemeth show to possess into a DR-worldstate the capacity to share three souls into one single body so the conclusion is that one body can have multiple souls.
Grey wardens can't absorb the souls of the Archdemons not because they already have a soul of their own but because their own will would not permit it.
It is what the witch said in DAI "a soul is not forced upon the will".
I don't know how Cauliflower is able to bypass this every time he reborn but i have to suppose that it is a form of blight magic and that his taint permit him to force others tainted beings.
1.
My impression was that the old god never told to the boy anything, however since they shared the same brain some of it's knowledge was floating into him in the form of memories.
2.
The old god inflicted pain to Kieran in the form of terrible nightmares every time he approached lyrium.
This may be a strong lore hint that old gods suffer lyrium and cannot tolerate it or that they had some problems with the Titans.
I don't see how anything else in your head is truly peaceful, but that's just me. 
I just expect him to be mentally deficient now, whatwith not developing properly for 10 years from birth.
I think he will share somehow the same issues of the Ancient elves.
Someone who was separated by a part of it's nature will feel lonely and different for life.