@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. 😉
It sounds like you are not going far enough for the Solas Quest. Those remarks are all you get when inspecting the bodies. Keep going past the claw mark body, you will find a Pride demon trapped in a circle and get a cut scene with NPC mages.
The Cole quest does glitch out and you can't complete it if you did not get all of his in skyhold cut scenes before claiming the locket from the war table mission. That's what you did. The only fix is to reload a save form before you got the locket and do the find cole scene then go get the locket.
