Is my family normal?
No. It's not normal, not at all.
I'm not going to create a fairy tale scenario here, where everything is just going on in your teenage mind.
Sorry for my blunt answer in advance.
At first when you mentioned your fights with your mother, I kinda did thought that it might be your teenage tantrums versus her parental control stuff and trust me until then your family was normal.
But it started getting weird when your younger sister (who's 14) isn't getting parental supervision and is allowed to grow like weed, needs some attention and care if she's expected to grow up normal and healthy otherwise it'll nearly destroy her future.
And when I read that your seven years old sibling can't read I think I got a really good idea of what might be going on.
Listen here sweetie, first - you need to separate the "parent" from your parents. I mean stop idolizing them as someone who gave you life expecting them to take their responsibility back in there hands. It's definitely not gonna happen anytime soon.
Instead just see them as people who do make mistakes.
They're actually broken people, people who didn't get to do or have what they wanted and all the frustration is coming out on you (and your siblings passively). There's no self love either.
Have you ever seen how when you press wax there's an impression left on it of your fingers?
And when you do the same to a stone, what do you think the result will be?
Yeah, no result! At all.
That's because wax is in the condition to get pressed whereas a stone isn't, it'll never be.
Similarly, you're being so much pressured because you're a pushover. Till you do that,nothing is gonna happen. No, not even their miraculous change of heart that you're probably expecting to happen one day. Take your own power back and refuse to be a doormat, trust me the day you start doing it, it'll be really hard, temptation of going back on the ground will be high since it's easier than confrontation. But it'll pay you off in some time.
Your mother needs to realize her own set of mistakes rather than playing the blaming game.
Also, try to get some job. I know it's hard to secure one job, especially in this time. But try to get financially independent as much as you can, it'll loosen their control.
Try to heal and protect yourself first. You can't serve from an empty pot.
Is there any government helpline number for counseling or something for your teenage sister, try to talk to them and see if anything can happen.
Also, although your mother is not physically abusing the younger ones but lack of love and care and constant neglect is a form of abused too, the silent kind.
I bet you if child services would ever find out about your sister being seven and still not talking and some other stuff that's happening there in your house, there'll be an action taken against your mother.
One more thing - Children are never mistakes. They're no legal or illegal children. The parents who brought them into this world have a moral are obligation to make sure their children takes on life healthy and happy(er).