Contact HoF

Even if you kick Morrigan out of the party in Origins, she always shows up at the end to make the DR offer. I'm not sure what she says about a Warden she didn't like in DAI, but she'll still say she's curious, I'm sure, and give you the HOF war table mission regardless.

That makes sense re: the Orlesian Warden since the three people who have ties to the HoF (Morrigan, Leliana, and Alistair) have no idea who that is.

Where the wiki gets its info on Cory being a ghoul, I have no idea, since all throughout DAI he is referred to as a darkspawn.

I do know that talking to Leliana if she was the LI unlocks the quest too.

And to the original question, I've had Morrigan mention that "We did not part on the best of terms" when she mentions contacting the HoF

Whoever wrote the Wiki has clearly not read the source books. In World of Thedas 1, the timeline refers to the Wardens discovering the intelligent DARKSPAWN Corypheus some 12 years after the death of Dumat. In World of Thedas 2 both the Architect and Corypheus are referred to as "intelligent darkspawn" and "ancient darkspawn" respectively. So clearly how Corypheus is referred to in DAI is correct in terms of the lore and how the writers intended him to be regarded. In fact as Leliana points out, essentially Corypheus (and the other Magisters who were with him) were the original darkspawn from which the others originated, unless of course you take the view that the darkspawn and the taint already existed prior to the trip to the Golden City, in which case they were merely carriers of the contagion into the world.

The essential difference between Corypheus, the Architect and other intelligent darkspawn and the rest of the darkspawn is that not only do they have intelligence but they seem immune to the call of the archdemon. In a way they are a different type of darkspawn from the regular mob and if the Architect is anything to go by, capable of transforming ordinary darkspawn into intelligent darkspawn. So from that point of view they are neither darkspawn, nor ghouls, but something completely different.

I don't recall they were asking the HOF for resources. I thought we just sent a letter asking if they had info. The HOF can, of course, ignore the letter. Maybe for your character, they would have flipped off the crow and kept walking, sending no response. I think most people would answer a letter, though.

The belt was just stupid though. I'd rather have received nothing, the belt is never any good.

A mortal who become a talking werewolf isn't an original werewolf(they don't talk and have no reason)Corypheus isn't a darkspawn.

My understanding is that one is BORN a darkspawn. From a brood mother. And a ghoul is a poor smuck that got tainted one way or another, like that dwarf in the deep roads  (Ruck) and Tamlen.

The Magisters fall into the ghoul category by my own understanding/definition, BUT...considering they have maintained a lot of their powers, knowledge, and even memories, and may have started it all, I'm going to just accept them as a special case of being Darkspawn.

He could do more than that, he could jump into a Grey Warden, which would result in an archdemon's death.

Honestly, I'm not 100% certain ghoul or darkspawn are appropriate terms for Corypheus or, presumably, the other magisters who blackened the Golden City. They may well be an entirely different class of creature.