Part of the problem is you think and love to deeply; otherwise, you wouldn't torture yourself this way.
"When you actually feel happiness and you still want to die; what does that mean?"--I don't know, I have and sometimes still experience this myself (don't worry about me though--my meds and therapy have gotten me to a point that I don't think I will make another attempt but I sometimes feel this way). Maybe we are extremely emotional people inside who have trouble venting the volcano that builds up inside of us?
"I can't be redeemed." -- I had a hard time with this as well when I was younger. But I know your situation is much more complicated. You are worthwhile. From what you've written, you have a brother and sister who look up to/love you. You wouldn't have earned their love if you didn't deserve it. I get along with my brother and sister but I have seen families where there are horrible sibling rivilries. Usually that's because one of the siblings is unkind.
Please hang on, you are worthwhile.