I find Cole pretty easy to understand, actually. Apart from what others have pointed out, let me point out that there are a few situations in which lose approval with him if you say something that's supposedly compassionate but ends up coddling him or dismissing his concerns -- which is not actually compassionate at all.
Cole is very much aware of how incredibly dangerous he could be, as he is aware of the fact that his actions in the White Spire were wrong. He may have been confused, frightened, unaware of broken from his true nature to the point of (almost?) having turned into a demon -- but none of that excuses killing these frightened mages. His desire to help and his determination to never again become a monster are his strongest impulses, and what he needs from the Inquisitor is to be taken seriously. Not reviled, feared or rejected for being who and what he is, but also not coddled, not babied (the way some people are all "my pwecious widdle bby" about him is really damn squicky and insulting), not wrapped in a blanket and treated like a mentally challenged invalid. He needs to know both that he is welcome and that you will stop him in any way you have to should he ever turn or be turned again. He is not a child, he is an alien being with a very strongly defined nature, senses and perceptions we can barely imagine but that are more crucial to him that sight and hearing are for us, and very different priorities. Yes, there are some complexities he can't grasp, but being different does not make him wrong or weird. As I said, I really don't find it that hard to understand him with a little effort.
With Ser Ruth, you're also dismissing her pain and leaving her alone with it if you refuse to judge her, which does not help her in any way. If there's anything "wrong" with the situation, it's not Cole's reactions but the fact that forgiveness is only available to a Inquisitor flagged as faithful. Mine is, and I really liked that choice, but a non-Andrastian should also have a similar option.
Other judgements have him favor execution over imprisonment. At odds with his nature? No, because he knows from bitter experience what imprisonment is like. Hopefully no one would be forgotten and left to starve to death in Skyhold, or subject to the sadistic whims of their jailors, but it's still a cruel and miserable existence both physically and mentally. A quick death is arguably less horrible than the conditions in a pseudo-medieval/fantasy prison.
As for the scene where he wants to put a dying soldier out of his misery? The setup is a really weird one because it happens at Skyhold, yet the way people are dying left and right and Cole's own remarks show that this is supposed to be the aftermath of the attack on Haven. It's one of the various annoying ways in which the game sometimes ignores time and distance. This scene should happen out in the snow, not weeks or months later in our shiny new fortress, but I guess they couldn't put it into In Your Heart Shall Burn because it would have broken the very focused narrative flow. Yet it also doesn't work as it is, in Skyhold, because of the massive timeskip. So I treated the scene the way I interpreted it to be intended, i.e. the immediate aftermath of a total disaster, and as a result had no trouble believing him when he said that there's nothing more that can be done for that man. Primitive conditions and the swift exhaustion of whatever limited resources the fleeing people managed to grab would kill many of the more badly wounded survivors.
Sometimes it seems that people blame Cole both for drawing any lines in the sand as to when to heal and when to fight, and for not drawing those lines often enough. He makes it very clear that he would rather not kill and finds it difficult, but those who choose to harm others have to be stopped. Having been hurt in the past in no excuse for hurting others in turn. Saving and helping those who are innocent of such crimes (or who have realized how wrong they were, stopped harming others and seek to atone) has priority. It has to have priority, or you just end up indirectly helping create more victims and suffering. Compassion doesn't mean wet blanket or punching bag -- Cole can't re-arrange the world so that cruelty, bigotry, lust for power and all our other BS "reasons" for causing each other harm suddenly stop existing, so if he wants to help the helpless, he has to make a stand against the abusers. And even in doing so, he -- unlike many -- does not forget that they are people.