Woo! A lot of text to go through here. Might have to make this a 2 parter.
1) He wants magic to be practiced freely without any regulations or oversight whatsoever.
The without oversight part was confirmed, but never the no regulations part. Solas approves of relatively free magical research. But we also know Solas has views on how magic should be handled (for instance, blood magic should never become a crutch nor a passion. Necromancy of intelligent spirits should be discouraged) and has voiced how people who have used their magic to harm or become possessed should have action taken against them. That, to me, does not sound like someone who wants magic to be completely unregulated.
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3) He behaved in a rather uncivilized manner towards the mages that tortured and turned his spirit friend. Yes their crimes are heinous, but we have the judiciary and we have prisons for a reason. My protagonist stayed Leliana from killing a spy because it was cold, treating people like trash. But when the moment came to stay Solas's hand against the mages that had done harm to his friend, I just feel my protagonist would have let him do what he needed to do. go ahead, Solas. A few strong words, maybe a punch or two. However, that doesn't mean I have to agree with his choices and he literally incinerated a couple mages that had no clue this elf was about to kill them. It wasn't a duel, it was calculated and swift rage. Meaning Solas, when pushed and hurt emotionally, resorts to very strong violence - Which is further reinforced in Trespasser where he reveals that he created the Veil and banished all the Evanuris for killing Mythal, which resulted in the doom of the Elven race as a whole.
Not to go off on a different tangent, but have you seen the judiciary system imposed in Dragon Age? Particularly for the Inquisition? There is no jury in your court. No people arrayed from which you can ask for opinions or viewpoints. It's you. You, the one who sits on the throne is the one who is both judge and jury.
This seems to be cases for other nations too. The Divine, the Emperor/Empress of Orlais, etc. They have the right to judge anyone brought before them with or without consensus from another political body.
Sure, you may have problems with how Solas handled the whole thing. I have qualms with it myself. But I don't see how anything Solas did was anymore "civilized" than you yourself do in the entire game. He was slighted, there was a crime (personal or otherwise), and the perpetrators were before him. So he dished out what he thought was judgement . You do the same thing the entire game (Servius, Alexius, etc.). The only difference was that Solas was not willing for the judgment to be handed to you, and there no fancy ceremony for it.
But as far the civility of it, Solas could have done a lot worse than incinerating them on the spot. They died in less than a second. He dragged it out no longer than was necessary. In general, Solas does not approve of making executions longer than they need to be, or making them a public spectacle. Just do the act and get it over with.
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4) He does not view modern Elves as his people and is practically indifferent to efforts made to strengthen Elf-Human relationships. Worse still, he has no problems killing the modern Elves, who are the result of his actions, because he wants to make the world safer for some ancient Elves .
Debatable.
Whom he views as "his people" is anyone's guess. Particularly depending on how Solas progressed in Inquisition.
We get confirmation that he starts viewing the elves as people if you befriend/romance him. But even in the rival scenario where he doesn't like you, there are hints that his world view changes to viewing elves as people regardless of his impression on the Inquisitor and vice versa.
We do get confirmation that he does care about elves (ironically shown in the disapproval scene), When confronted about how he has abandoned them, he disagrees--though he does say he simply sees no way help them as they are now. He also disapproves if you claim that he doesn't care.
We also get confirmation that he is not indifferent to all attempts to strengthen Elf-human relations. In addition to approving if Briala rules alone, he also approves if you get Celene and Briala together. He also makes remarks on Clan Lavellan being wise enough to include themselves in involving themselves in human affairs.
Furthermore we get confirmation that he does have problems with killing modern elves for his plan ("I take no joy in what I must do"). Or at least if you befriended/romanced him. I am currently to tired to investigate the rival cutscenes on the matter, but I'll assume nothing was said indicating open remorse for a disapproval inquisitor.