I have not heard that it would be outdated as a concept.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.