In the anime , would Kaede live with Kouta her life happily without killing or hurting others in the end ?
Hard to say.
Old habits die hard. Lucy spent her whole life surrounded by violence and hate. Kicking that habit out, especially with Yuka around will be difficult.
Regrding Kouta... While he may have been more understanding than in the Manga, he has by no means forgiven Lucy. Far from it. However, he also admits that he loves her. They could start something, but I can't see it as full fledged relationship. Moreover, it will be a bit of a "Mind Game Ship" and it mostly depends on how much Kouta can help Kaede keep her darker aspects as Lucy in check.
That said... It is entirely possible that shem by destroying her second horn against the soldiers, intentionally killed her Lucy persona, and also might have sealed the DNA Voice away, and established Nyuu as the new main persona so she can live in peace with Kouta and the rest of their family.
Understood , even if Lucy kept with her personality I think she can control her murder instinct if she stays on Kouta's side like Nana did
Again, it'd be hard. Not impossible, but difficult.
I doubt she can, Kaede has shown throughout the series, on more than one occasion, that she has almost no emotional self-control or restraint, opting to lash out at people for the most trivial of reasons.
She has also no sense of taking responsibility for her actions, opting to lay the blame for all of her suffering solely on others, claiming that she had no choice because the voice was telling her what to do, it isn't until the very last that she pulls herself together.
A relationship between her and Kouta is never going to grow into anything beyond good friends, she simply caused too much harm.
That's also true. It's only with Kouta that she learns a modicum of restraint. And even then... The DNA Voice can still take over if she so desired...
I hate to say it, but it seems the only way for this to work is to have another being or beings exerting overwhelming power over her, insuring she can not go back to murdering innocents without suffering painful consequences for it...
But she said that she wanted to forget everything and be beside Kouta , she said that before he hugged her , so this may be a proof of new life for her cuz she want a new life with Kouta
Perhaps she might gain true restraint if Kouta demanded she learn to appreciate all the others the way she does him, and starts to regard them more highly, and thus other people outside Maple House as well.
Yet, even if all that occurs, Kakuzawa and his schemes are still waiting.
That's another possibility. Will Kouta succeed, though?
He's in a unique position to. Also, once his memories are back, perhaps he'd become more decisive, no longer forced to hover between reality and memories too painful to process. I can actually see a scene wherein he lets Lucy have it verbally, reducing her to tears that Yuka ends up comforting.
That also begs the question if Kouta will let Yuka know what Kaede had truly done...
In fact, what would Kouta even do now? If he, say, elopes with Yuka or Nozomi, can he make Lucy accept it? Or is that just a time bomb waiting to blow up?