I think of one who do not kill or injure other people, even when they are bandits.

In order to deal with situations where there are people, Illusion magic or is there another way?

But ghosts, vampires and the undead should be vanquished.

But how? I have heard much bad about Destruction, that you are not able to kill things because you need to make overpowered enchanting and potions.

My character doesn't want to use enchanting at all or potions, only poisons.

So how to vanquish the evil?

So, your chacarcter is Batman and Cicero The Joker? Well, if you're on PC try to look for a mod where you can knock out NPCs.

A fun way to do what you are wanting here is to get good restoration and use a good follower. Illusion is a perk and magicka heavy skill to use well so it is hard to develop too many other skills. but you could get fairly good with onehanded to use just on undead. it is much easier to beat down a draugr when it is turned. The idea is to use Restoration when facing undead as you won't have a magicka conflict with Illusion as it won't work and the rest of the time try to use Illusion, which is great on animals. I suggest considering hiring Mercurio in Riften asap as he is really great on undead and can help with that until your restoration skill gets good enough. There are ways to level him up if you want or just dismiss him if he becomes under-leveled and get housecarl or merc tank.

Just saw that part about poisons, not sure where you are going with that as it sounds absolutely exclusive to playing without harming anyone..... it doesn't work on undead or vampires.

I don’t have that issue with Destruction, but then I rarely play above Expert difficulty. There are some useful spells in Restoration for undead. A follower is great for chasing down turned undead, but they tend to kill bandits. You could use Conjuration for direct damage if you want to go another way.

Illusion, Sneak, and Restoration (healing himself while running away) is how my no-kill mage character dealt with all conflict.

If you’re using poisons it suggests a weapon skill. If killing undead is the goal, I’d skip the poison and use an enchanted weapon that you find in the game.

http://www.nexusmods.com/skyrim/mods/52681/?

Unless you play on legendary, you won't have to worry too much about destruction, just make sure to get your hands on spell cost reduction equipment and try to get stronger spells (if not in college, then from court mages) soon. You might also want to consider investing into augmented fire, good against many undead.

Illusion spells are great, school offers several ways to neutralize an enemy (fear, calm, invisibility and muffle, paralyze), and poisons are also an option, put some fear on an iron dagger and cut an enemy.

You might also think about having a decent speech capabilities, as it can offer a more peaceful result out of many dialogues.