1- This is largely debatable in the moral of the story and yours as an author... And there is really no way I think anyone could answer this.
Morality is subjective, what you think is right is not nescessarily what I think is right, and the same goes for every other person in the world, no two people think exactly alike on every subject.
Normally you can separate it by plot-focus vs character-focus,
The rule of thumb for me is, everyone is the hero of their own story, even the villains, so it becomes more of a matter of perspective than a matter of inherent good vs evil as such a thing does not exist in the real world.
2 - A picture is worth a thousand words.
There is most certainly a wrong way of doing a good thing, like sure killing all criminals in the world would end crime, and having no more crime is an objectively good thing, but then people would constantly live paranoid of what exactly constitutes as a crime and become inert, living in perpetual fear of whatever is killing people.
Funnily enough this a big theme across my whole story and even my villains were made to constrast with the hero in this exact point, both want the same thing, with widely different views and methods.
3 - Villains are meant to be human too,unlike monsters who are just 'evil by nature' a villain is making a conscient effort to be like that, and exploring those conflicts will naturally lead a reader or viewer to relate to the villain even if not agreein with them, they must be thinking, they must have a goal, and be an active enemy to protagonist.
So to answer your question, it is a REQUIREMENT that the reader or viewer be able to relate to the villain in some way, otherwise they will just feel inpersonal...
A force of nature that corrupts and kills anything it touches is not a villain, it is just a monster, mindless and uncaring, it has no desires, it does not plot anything, it is just there.
A villain has to have a motive and humanity to them, even if that humanity is corroded beyond belief and they are almost a mindless murdering machine, a husk of the person that once was... So long as they can still think, they are a villain.
For the secound point though, villains don't always need to be reedemed, it can be entirely satisfying to have them killed off in a blaze of glory and spectacle... To let the reader feel the catharsis of 'it's over' and move on, sure your protag might not be the killing type, but that is even better as you can write in how the villain offs themselves.
Similarly sparing them is great too as it opens up story possibilities, to explore their broken psyche learning to heal and becoming a better person than they ever gave themselves for is equally cathartic... So yeah, both are good ending for different reasons... Ops did I go back to point 2? xD