Profound questions, hard to answer.
A lot of words have seen their meaning change with time and generations passing... A pejorative word today can be a compliment tomorrow. And vice versa...

For the use of an insult, however you take it doesn't change the fact that it came from a hateful person - or at least it was his state of mind at that time (except from irony and mockery, that can be done between friends), who was aiming to hurt you. If you take it any other way, good for you as it passes through, but I don't think it can change the intention of the person who said it. If you don't react to it, it can make him feel unheard, or not understood, feeling his opinion doesn't matter, and that can either make him let go or reinforce his hateful sentiment.

To try to answer your last question, an insult stays an insult, whatever how the receiver interprets it. But the way the receiver reacts can change the opinion of the insulter, but only with communication. But with some people, communication is impossible.