I really must return when my likes are refilled. 
I would want Cole to meet Justice or Merrill. Justice, because it would be interesting just to see how they would react to each other. Justice and Compassion does compliment each other rather well. Merrill, because she seemed very interesting in the spirits, and he could give her that up close study. That relationship probably would go way smoother than Liara and Javik relationship.
These are the two I'd most want him to meet too! Anders as well. Merrill was the first character I remember having an open-mind about spirits, so I don't think she would be put off. Like you say, she'd probably be very interested on an intellectual study. I think they'd also get along great on a personal level. Both are very sweet, and I think Merrill's desire to help her clan, even at the cost of her own life would appeal to Cole. Maybe he could help her to heal too?
Part of why I'd like to see Cole with Justice is because we only ever see snippets of him speaking with other spirits and helping them. I'd love to see him trying to help a fellow spirit, if that can be done. Could he use his powers on one? Since Cole came so close to having his true nature corrupted, I think he'd definitely understand what happened on a personal level. We never really get an opportunity in DA2 to understand what exactly is going on with Justice.
I'm very glad it was not implemented, not only because it would have been horrifying both in that scene (apparently Cole would essentially have tortured the ex-templar to death in front of our eyes) and in the eventual outcome (Corypheus taking over and making us kill Cole), not only because I generally dislike nonsensical "evil" options, not only because I can't imagine either Solas or Varric stand by and watch it happen ... but also because Cole is (despite the bittersweet nature of his quest) a hopeful and positive character at the core and should be allowed to remain as such. Not everything or everyone has to be tragic and bitter and grimmedarque. And I say that as someone who does think Inquisition is way too smooth sailing and needs more setbacks, and as someone who can't imagine any ending for Origins other than the ultimate sacrifice.
Same here! I am eternally thankful that they just kept Cole's development as 'more human' or 'more spirit'. Even if one did lead to him becoming corrupted, it would be heart-wrenching, but at least it was only done with the Inquisitor's best intentions. Encouraging him to become demon-like would be such a malevolent thing to do. More evil than anything Warden/Hawke can do, imo. Even in DAI's neutral/grey choices, that one thing would make the Inquisitor the most potentially evil for me. 
It's bad enough with the option for Hawke to sell Fenris back into slavery, but corrupting a spirit of compassion like that? A being whose only desire is to help and heal? *disgusted noise*
That is where they colosally screwed that scene up, yes. IMO the best cutscenes with a companion/advisor are usually the ones that show closure and connection by ending with a shot of the two characters together. It doesn't have to be a happy kind of togetherness, that isn't the point -- one character quietly supporting another character in a difficult moment by staying with them is just as poignant and important, if not moreso. They did this with Cullen's (friendship/platonic) scenes, which is one reason why I ended up liking that character a lot more than expected. Cassandra's friendship scene in the war room ends that way, too, and I absolutely love it. Just a few quiet seconds of companionship help the bond feel real and tangible in a "show, don't tell" kind of way that is often worth more than words.
*snip*
I just wanted to say this entire bit sums up perfectly how I feel about that scene! Such a let-down after how perfect his 'dinner' scene is ("...thank you for helping me find this again, you don't know what it means."
). The tiny snatch of dialogue during the after-party is the one shining light after that. Knowing he's happy and safe (at least for now), and planning to stick with the Inquisition when most people are bailing.
Good to see you in here again too, btw! 
In regard to your point about the Nightmare demon - I think it would've had more impact if our companions had been trapped in nightmares again, like DAO. It's a lot easier to remain confident/brave when you're surrounded by friends and simply being trash-talked. A lot harder when your mind is being warped!
(I tend to focus on Dorian because he's my fav, so pardon me.)
*snip*
I've never seen the spirit path and am sorry to learn that Varric reacts this way =/.
I like that!
I don't find many in-depth looks at Cole and Dorian's interactions. It's a real shame, considering that they have one of my favourite friendships in the game. I really wasn't expecting them to get along well, especially since I heard Dorian's banter with Solas about 'spirit servants' in Tevinter long before recruiting Cole. I thought he might view Cole as a tool or something sub-human. Instead, there was some wonderful bonding and insight there. It comes second only to Cassandra's friendship, for me.
I like to think Varric eventually sees that he hasn't really lost Cole, especially since he's still at Wicked Grace. He might be a little more wary because of the whole Anders thing, but I doubt he'd stay that way forvever.
There's a poignant tragedy to Justice's fate, that in trying to help a friend he's ultimately destroyed, twisted into something so terrible that hundreds are destroyed as a result. And his friend is ruined and broken and destroyed right along with him; it always breaks my heart.
This affected my choice for Cole too. It's so tragic to see a spirit (especially one you've befriended) being twisted from a good purpose. I spent ages wondering if making him more of a spirit while he's living in the human world would lead to that problem. Or whether making a spirit more human would force the problem. I am so glad that the choice seems to benefit Cole either way (even if some part of himself does become more muted).
Cole romance fic?
*snip*
(Seriously, do what you want. Just know that I am morally obligated to oppose you and everything you stand for.)
I once went hunting for Cole/Inquisitor friend-fic and found that the most popular was a smutty fic.
Yeah. Not quite as bad as when I looked for Hawke/Bethany friend-fic, but Cole/Inky is a definite 'notp' for me. I tend to see him as asexual and aromantic anyway, but pairing him with the Inquisitor feels particularly off. Their bond in-game feels a lot more like a strong platonic friendship. Like family.