how should I respond and act towards people who have betrayed me . . .
I know that I should love and not hold any negative emotions towards other living things
Being angry with someone that betrayed you is proper. It is also proper to make sure that that does not happen again. (I mean, that they do not betray you again.)
when a person writes to me, of whom I know that he/she holds ill thoughts towards me . . . and when I answer to those questions with something like this: "You know the answer, why you ask me it? " . . .
They reply always that I'm retarded and make no sense
Yes, that specific person will tell you that you are retarded. That is betrayal. He/she betrays you. You point out that they do something wrong, and then they say it is your fault. They betray you again.
So it is no use to write back to them. It is no use to explain. As you say, they already know.
And another thing, I was wondering, if I don't make up with them, or be friends again, like giving 2nd chance... ( here its 3rd and 4th...
), does that makes me a bad person
No. It is proper not to be friends again. You explained already: It is impossible for you to make up with them. You tried, and they called you stupid.
If they wanted to make up, I would not even react.
. . . if I don't make up with them, . . . does that makes me a bad person or does that mean I keep the past with me and think ill of others?
From what you write, it is obvious that you repeat things if you make up with them. So, if you want to leave the past behind, to not make up with them.
If you come to the logical conclusion that someone betrayed you, then you are not thinking ill of that person.
If you are angry that someone betrayed you, you are OK.
It would be bad to allow your anger to grow and grow and grow and then kill somebody.
It would be thinking ill of somebody if you hoped that they would get an accident.
Sometimes a situation brings feelings in us that we would not want to have. But specific feelings belong with some situations. Like when someone dies, one can be sad. That is OK. Or if someone marries, one is glad. That is proper. That is not negative or positive - it just is what should be there in that situation.
Meditation can help to see the feelings in perspective. But they are there.
'Coz the reason i don't want to make up with them is that I know already the outcome...
Indeed, you know already.
hope that ignoring, won't make me more arrogant then I am right now :/
Can you explain how you are arrogant?
(I suppose that you are not arrogant at all, so I would like to check.)
With this all, I come to the conclusion, that you see the situation quite clearly. You are unsure about yourself, but you see the situation (and the misbehaviour of that person / those persons) clearly. Very well.