I've been wondering. What would Cullen think, do you think, about a Lavellan Inquisitor acting as a sort of Keeper to the Inquisition's elves? Telling them about the Dalish and their beliefs, and giving those who were interested a chance to convert and be ministered to?
I don't think he'd mind, since Cullen never tries to push his faith on anyone and seems to respect other religions as long as they respect his?
His comment about the Qunari and Dwarves beings heathens in Origins and DA2, I think is based more upon the fact that those two races tend to follow practicises that are so far removed from the theistic religions of the humans and elves? For example, the philosophy of the Qun rejects of any kind of divine force in the world, while the Dwarven religion eschews a singular creator, in favour of a belief in the Stone and Ancestor worship?
He'd probably consider Sky Watcher to be a "heathen" as well despite the Avvar having Gods, due to their Animistic beliefs that their gods exist in nature all around them and can communicate to them through signs and portents?
But I don't think this this is down to him being close-minded or disrepecting their beliefs exactly, I think it's probably just a case of culture clash and his being unfamiliar with interacting so closely with various races and cultures? For the most part, he spent the better part of the last decade in a closed environment among fervent Andrastians, so you'd expect him to be less cosmopilitan than someone like Hawke, who grew up in a village that traded regularly with Chasind and has former Tevinter slaves, Rivaini pirates, Dwarven merchant princes and Dalish Elves counted among their friends?
Ooo, that's some good dialogue. But, why would Hawke be going to Weisshaupt? 
Pretty much the same answer as what Ninetozero said already, but it's also worth noting that if Hawke's sibling is a Warden, it's mentioned that they were already heading to (or already at) the Anderfels border when last they spoke? It's likely that they might have arranged to meet up along the way?
Actually, if Hawke's sibling is a Warden, I'd like to imagine that Bethany/Carver was originally working with the Warden-Ally to stop Corypheus? It seems in-character that Hawke might have offered to substitute themselves in their place, as long as their sibling agreed to get out of danger and head to the Anderfels to let the other Warden's know what was going on? Plus, Hawke has already defeated Corypheus once and not being a Warden means that s/he was not in danger of being compelled by them, meaning they could serve as a check for the WA if they ever felt they were falling under Cory's influence?