When I don't do the washing up, or take out the trash, or whatever when mum asks, she charges me $10. I have a job, but am 17 living at home.
I am wondering if she is allowed to make up fines for not doing work and taking my money that I made myself (I don't get any allowance or anything). She originally charged $5 but bumped it up to $10 recently. Today, she is telling me I need to give her $20. She gets money from the government through child support too.
Is she allowed to charge me money?
I think the question here is, do you want to be an adult?
If the answer is "yes" then you need to sit down with your mother and ask to agree some basic rules. The main points will be:
Who does which bits of housework and when.
How much you will pay for room and board out of your wages.
You should also discuss a savings plan; you may find she is happier to accept less money for rent if she can see that you are putting it into savings instead. I don't know what your longer term plans are, but sooner or later you will want to move out and having some money in the bank makes that massively easier.
As @anongoodnurse said in the comments, it sounds like your mother is trying to motivate you with the fines. However financial penalties of this kind can backfire badly. You need to try to negotiate your way past that. Make it plain that you are willing to do your share of the work, but financial penalties of the sort that she has been imposing (especially if she just makes them up on the spot) are not on the table.
Having an agreed set of rights and responsibilities for both of you is the first step to being treated as an adult. The second step is sticking to it. Part of being an child is having parents nag you to get on with stuff. Part of being an adult is making agreements and then sticking to them.
You may encounter some resistance over this; your mother considers you her child and is used to treating you like one. Getting parents to shift into adult-adult mode can take time and persistence. It helps if you can learn to spot parent-mode talk and then make a conscious effort to respond in adult mode instead of child mode.
OK, I'll bite.
Is this allowed?
Legally speaking, this probably isn't 'legal' because there is no preexisting contract stipulating fines for future events unless you agreed to these conditions verbally. Contracts is being used in a loose manner here and imply written rules and reasonable ability to understand as well. There doesn't have to be agreement by both parties to proceed.
For example, you can't park in a no parking zone whether you've agreed to that law or not. But the rule has to be posted, or there has to be a reasonable expectation that you understand the rule having learned it in the natural course of, say, learning to drive (e.g. you can't park in a manner that blocks someone's access/egress regarding their driveway.) That's why ignorance of the law is not an excuse.
However, not everything that happens under the confines of your roof is governed by law. This may be a case of, "My House, My Rules", which means if you don't like it, move out. Is this legal? Yes, it is. At your age in most countries, your parent(s) can make you leave for almost any reason whether you agree to it or not. (there are exceptions, but your question gives some evidence that these exceptions don't apply.)
I don't think this situation is really about the law; it's about a particular parent-child relationship and conflict resolution. Someone is probably not doing their chores, and someone is probably frustrated enough to start levying fines. If you do not like what's going on, you need to have an adult-to-nearly-adult sit down with respect, honesty, and give-and-take on both sides.
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.
