Is it normal to hate my whole family?

I come from a family of 5 kids,though we don't live together. Since I was born,my parents have never been together.My dad is married to my step mom and they have 3 kids,two boys and one girl. My mom has my sister and I.

Since I was born,I always thought my dad was the one who cheated on my mom since my sister is the first born,then my half sister then me, followed by my half brothers. But when I was in seventh grade,I always had a feeling that there's something my mom and sister were lying to me about something and after thinking for sometime,I came to a conclusion that my 'sister' is actually my half sister.My 'sister' had always been looking down on me and she still does till now.She's really bossy,lazy and dirty so I end up doing most of the work in the house.

When it comes to my mom,she really loves my sister more than she loves me. And it sucks. She always calls me stupid and tells me that I don't think straight yet I'm more intelligent than my sister. She is a spa therapist.They always talk badly about my dad not minding that I'm around.

I kind of prefer my dad to my mom but I hate him too. There's this time when he took me to live with him and he used to beat me up with a belt on my back and I used to cry a lot coz he never punished the other children for the two years that I lived there. He even made me repeat 5th grade though I had qualified to go to the next class and when my brother was told to repeat 1st grade,he paid some cash to the principal so that he could not repeat. He works as an engineer and a lawyer though he only sends money to us when we force him to.He doesn't even like buying me things yet he knows he can afford them but when my half siblings ask for anything,he doesn't hesitate to buy it.

I hate my stepmom coz she liked exaggerating stuff to my dad so that I could be beaten.

My half brother always went telling everyone that I'm not even his mother's daughter and he braggs a lot like: 'do you know that I went with dad to USA and Turkey... He even bought me a PS'.

My half sister is a total bitch. She used to gang up with her mom on lying to my dad about me.

I only love my youngest brother. And he loves me too...more than he loves his sister and brother.

Back to squire 1. I came to confirm my suspicion about my 'sisters' identity when I went to my mom's room and looked at her birth certificate that they had been trying to hide from me.I now know the truth although nobody knows that I know. And it turns out that it was my mom that cheated on my sister's dad and I was born. And also I'm my dad's illegitimate child. And in short I'm unwanted in both sides.
Any time I try defending myself from being insulted they say that I complain a lot. She used to give slaps on my back like two one year ago but she stopped and I'll tell you why.

So late last year,I had back aches but I didn't tell anybody coz as usual they say I'm lying since I don't want to work. And this year,I was diagnosed with scoliosis when it got worse at school and I was taken to hospital and now I shouldn't let my back go through anything.

But I'm used to it already and I plan to look for a university scholarship in another country and go for good and when I've prospered,I will come back and give them the money equivalent to what they spent on me then go away.

And sorry for the length.