Today, she is telling me I need to give her $20. Is this allowed?
You're asking the wrong question (I know I'm not supposed to say that, but I'm saying it anyway).
You're obviously looking for someone who tells you that this isn't right so you have some backup against mom. So okay, here's it is: In my opinion, this parenting strategy is at least questionable, irrespective of whether it's legal or not.
This doesn't help you, however. I don't think it's questionable because it's unfair; I think it's questionable because it's not teaching you the right things. It's teaching you that you don't have to help as long as you pay. We've monetized many other aspects of life already that some of us don't feel comfortable with; that your mom does it in your family makes me think everything else failed and she's desperate.
So, think about what will happen if you go and tell mom that what she's doing is wrong because you've heard so from the internet and that therefore you will no longer pay these fines. The result will be an escalation of the conflict. She might stop buying all the stuff she's (probably) buying for you, or stop doing all the stuff she's (probably) doing for you. Maybe she'll make you cook your own dinner. You'll retaliate by eating whatever's left in the fridge. She'll escalate, then you'll escalate, and in the end you're somewhere you really don't want to go.
So I'd suggest to be adult about it, like Paul Johnson and Anongoodnurse say: Discuss your misgivings with your mom, and do your part of the work (or just do your part of the work, because then the fines will go away all by themselves...). Don't even try to look at this from the financial side of things because you'll lose; child support and $10 fines don't even remotely cover what you cost your parents.