I believe to remember that the contract is valid if a minor of that age typically has that amount of money available and can understand the consequences of the contract. So the business owner does not need to know how much money the particulur kid gets. If the particular kid gets exceptionally small pocket money the contract is valid and the parents are responsible for its legal implications.
Of course what is typical for a certain age might end up for interpretation by the courts in the worst case (and occasionally it does).
I have not heard that it would be outdated as a concept. What would be the replacement? To my understanding it is generally recommended the give minors some money. And parents should not interfere much even if they disagree how it's spent.
What the term would be in English speaking countries I have no idea if pocket money sounds archaic. The translation sounds good to me not being a native speaker.
The sum might depend a lot on the country. I have no contacts to 16 year olds so I can't tell.
https://www.wiado.de/taschengeldparagraph-was-ist-das/ has a table. It doesn't look completely unreasonable for Germany. Please note that this is not a law, so if a case goes the court the judge might come to slightly different figures.
Of course what is typical for a certain age might end up for interpretation by the courts in the worst case (and occasionally it does).