Ok so I'm going to do Dorian and my Inquisitor Cyrrith for 7 and Lucanis and Velanni for 15!
7. Has there been any sort of betrayal within the relationship that they've had to overcome?
No like major betrayals but for Dorian and Cyrrith they get into a nasty argument after Cyrrith's clan is destroyed and Cyrrith's father shows up and berates Cyrrith for not coming in person to aid Clan Lavellan. The part of this that Cyrrith considers a betrayal is Dorian basically saying that it wouldn't be the end of the world if his sister was enslaved. It was meant as a comfort on Dorian's part but it does not come across that way to Cyrrith.
The argument isn't the part that's the betrayal for Dorian. After said argument Cyrrith sneaks off and finds a Dalish Clan that he spends almost a week at. He of course did not tell anyone about this.
When he gets back him and Dorian have a conversation about it bc Dorian is fucking hurt that Cyrrith ran off without telling him when he thought they were going to talk the next day. (all future sneaking away is Dorian sponsored even if they've fought).
Then there's the whole 'putting on a brave face when suffering instead of telling someone' thing that Cyrrith does. This is mainly about the mark nearly killing Cyrrith and not telling Dorian but it also applies to while they're separated during Veilguard because Cyrrith ends up having a huge breakdown that Dorian wasn't expecting.
15. Would they let the world burn for their relationship or would they make sacrifices for the greater good?
With Velanni there is no doubt she would let the world burn for Lucanis. She might even set the world on fire herself if she felt like she needed to. She ended up tricking Solas, knowing it might backfire, because she was so pissed about what he did to her and Lucanis. She's never claimed to be a hero, she's actually been very vocal about not being one. She's a Crow and she's going to do things like a Crow.
Lucanis is also a yes. This is the man who said he would kill every blighted creature in Thedas to keep Velanni safe. He's also a Crow so they're very similar in how they react to people they love being hurt. I do have it written somewhere that him and Spite become so ferally angry when Solas steps out on Tearstone instead of Velanni that they attack him. Like the island is being destroyed around him and the only thing that matters to Lucanis and Spite is Velanni.