Re: Issues with Cole and Solas "inner circle" quests.
@Tsurugi-ijin What system are you on, and is your game patched completely? (Patch 11 for PC/PS4/XBox One, Patch 8 for PS3/Xbox 360... I think). This sticky might give you an idea of what information is helpful to include 😉
Unfortunately, I've never seen anyone who has one of these issues get past them and then gain the ability to fix them, I think that once it's broken, it's broken, the only chance to fix the bug is to load a save before it happens.
Tips that seem to have had an impact on others with these issues: with Cole, I think some people experience the bug with his quest because they needed to have other conversations with him before handing over the amulet. With Solas, you shouldn't need to investigate corpses or anything (this may have been a fix included in a patch, as I remember you used to have to do that), as soon as you get near the demon a cutscene should trigger (I tend to come from the Dalish camp, through the river, for that quest, I never see any of the dead people).
Sorry I can't offer better news, but hopefully this will help prevent these bugs popping up in future playthroughs. 😉