Addressing your first point, I'm not 100% on the legalities of the way I'm trading and I haven't found anything about UK laws on parents consenting for minors to trade under their name. My mom has consented to it but has never personally touched any of the accounts I've created. Everything is set up on my own devices (PC and mobile exchange apps) Do you think they could trace my IP and I could get caught? I'll deactivate all my accounts under my mom when I do turn 18 (unless she wants to start trading / investing herself) although that will probably look fishy when I transfer all my coins / fiat.
My assumption is that what you are doing is illegal, and I would have to advise you to stop; I cannot control you and I doubt they would shut you down or investigate further based on anything to do with your IP address. However, if it ever became relevant to law-enforcement or taxation purposes and gets investigated further, your mother may have consented to you impersonating her and operating under her information, but this (as far as I know) does not make it legal, unless she were the one doing the trading, funding and exchanging. If you are under the legal age for using the exchanges, I would just use 3rd party exchangers from this website and operate with a wallet as I've already suggested; this would be perfectly legal (again, as far as I know). I'm not giving legal advice, and I would advise you do get legal advise if you plan to continue this way. My advise would be to wait until you are of age to legally use these services, or use an alternative that is legal and available to you. There is nothing fishy about transferring your coins, almost ever, but again I'm not condoning or helping you figure out how to operate illegally.
Secondly, I understand the risk of keeping my coins on an exchange. I've just been lazy and haven't researched whether it would actually be worth storing such a small amount of coins in a wallet. Literally I have like $3-5 dollars in each of the alt-coins I listed so I just assumed it wasn't worth it with the fee of transfering these from binance to a wallet.
Always assume it's a good time to buy BTC? Could you explain why, I'm confused by this statement. Even when it was at ATH in Dec?
Yes, even when it was at the all time high in December. Time is on our side, and unless you believe that bitcoin will never increase in value from where it currently is (at the time of your buying) then it would make sense that it is always a good time to buy, until such a time comes when you believe Bitcoin has bottomed out and will no longer increase in value. Was it a good time to buy Bitcoin at the ATH prior to December? The answer is obviously yes, because ATHs are consistently broken by bitcoin. Not a year has gone by that there has not been tremendous strides made in terms of the price of bitcoin. If you bought Bitcoin at $20,000 then just hold onto it, don't sell it at $8,000; assume it is always a good time to buy bitcoin and you will never get caught in a bad sell of bitcoin. You can disagree with this logic, but it seemingly has tremendous benefits.
Do not procrastinate the security of your finances unless you will be able to take the loss with a smile on your face. Laziness is no excuse, but you are correct that it might not be worth it to store such a small amount of coins on a wallet if you are planning on liquidating them for fiat sometime soon. If you are planning on holding them, which I suggest, then you would be infinitely better off holding them on a wallet in which you and exclusively you have the private key and encryption password.
If you enjoy holding multiple alt-coins then you should probably have a separate wallet for each, unless they are ERC20 Ethereum based tokens that can be held on one address/wallet. Normally most of these alt-coins have very minimal transaction fees, so security is always worth the few cents you may lose to transaction fees. If you regularly are changing which coins you are holding and like to exchange things very regularly then feel free to keep it on the exchange, as long as you are aware and acknowledge the risks you are taking on.