Hm, I guess I sort of meant knowledge and memories. Like his view of how demons are definitely bad and that he was pretty sure he wasn't one, but at the same time wondered if Rhys was one tormenting him. I suppose he could have learned that from the mages around him instead of from the original Cole though. It just seemed more like it was ingrained, like being taught it in mass at the chantry or whatever the Thedas equivalent would be.
As for being 15, I vaguely remember somewhere it saying he was in the Spire for years. So at least 12ish when he got there + "years" + the year of knowing Rhys and murders. So we don't know for sure, mostly because we don't know for sure when the templars caught him, or how long "years" was.
Ah, yes. I assumed he learned it by listening to templars, watching the mage's classes and the fear that was instilled in him from original Cole. I can't remember but doesn't his dad call him a demon for being a mage? That could have also simply been the nightmare talking. But yes that could go either way in terms of how he learned that. He also could have learned it from Rhys. They also have a Chantry in the Circle don't they? He could have watched/listened in on those too.
Really I guess it's all a big question mark haha.
Okay yeah. I assumed he'd be younger cause a lot of people are claiming he's about 15ish years old and I've never been certain where they got that so I just assumed it was stated somewhere.
I just finished the book a couple of days ago and yeah you are right Lambert didn't use it he just showed it to Cole and asked if he knew what it was.
Also I wonder myself why they put the circle near where a veil is thin too...not very smart. lol
Hmm... Yeah, I wondered about that too. But if I remember right, Lambert doesn't read the Litany or try to go after him, does he? I mean, it is possible as others suggested that by realizing what he was, he realized he could enter and leave the Fade at will, since Shades are able to do so as I understand.
Also, on an unrelated note, what is with the Templars/Chantry putting Circles in areas where the veil is thin, and continuing to execute their mages inside said Circles (which also thins the veil). You'd think they'd eventually have figured out thin veil = demons. Demons + mages = bad. Hm.
Lambert uses the Litany at the beginning of the fight to dispel Cole's invisibility. Cole fades away after the battle's over, moments after realising that he isn't real. I doubt Lambert predicted it. The reason why I don't think it was his regular invisibility is because Rhys would've still been able to see him, like he's always been able to, but he saw Cole fade away in front of him.
Kirkwall's veil is ridiculously thin, and yet they put a circle there, only to be surprised by all the demons and possessions that happen. The only explanation for Circles being there is that the people in charge weren't very smart.
Meeszy explained it but just to specify this point, cause Lambert does use it...
To quote Asunder from page 457:
"Invisibility is an interesting trick, I'll give you that. Of course, every trick is worthless once the truth is revealed." He put away the vial... and took out a small book. It was an odd thing, the size of his palm and bound in shiny gold. The man opened it and began reading aloud. The words were old, Ancient Tevinter... almost a chant, really. ... Then something changed. The tingle of magic, pricking along his neck. It swept through the passage like a wind, and with it went the shroud that hid them. Cole gasped in shock.
Lambert throws the book to the side, and beats the crap outta Cole. After he's done with him he picks the book back up and then simply shows it to him and calls him a demon. Then Cole *poofs* after realizing he "isn't real".
I wonder if Cole has some how become, basically, a ghost? It is a belief that when you die your spirit/soul/whatever you want to call it gets sent to the Fade for a short while, correct? (At least I recall Wynne saying something like that in Origins, my memory sucks.)
Sooo, put on your tinfoil hats for this;
What if there was a shade feeding off of Cole before he died. But when he did die, his spirit/soul/whatever got attached to the demon somehow? Taking on the persona of Cole (essentially the spirit) but the form of the shade. A living ghost if you will?
Okay, crazy theory done. 
It's possible. I don't think Cole is a normal circumstance. If the world of Thedas has souls I think it's a good theory. ^^
Why was Cole affected by the Litany, but Wynne/Faith wasn't?
In Asunder? Wynne isn't around during the fight till after Cole *poofs*. Therefore she wasn't in the area when it was used.