Yeah, minors don't get the cash, just adults who are of working age.
$10k isn't nearly enough to sustain yourself, so a basic income of $10k would probably be a failure. You need to make it high enough for it to be equivalent to some sort of level of living where you can afford food, shelter, and the necessities.
But low enough for most people to want to work on top of that income and make more. So you don't make it $50k, because then a lot of people would just sit on their butts. I don't know what you make it exactly, it depends, but you get the idea. The incentive has to remain there for most people to want to work to make more. Nobody likes living on the bare minimum standard of living, right? Some people will do it, so the key is to balance the amount to something that will maximize people wanting more, while still giving them enough to get by.
Basic income is basically a replacement for the welfare system, not free money to give to people just because. It's supposed to remove large chunks of poverty (nobody's going to be on the street anymore, homeless, and not being able to feed themselves, etc.) and is usually supposed to be more efficient than the welfare and charity systems at achieving that. Since first of all they're not even achieving that at all right now.. and second of all it's supposed to actually be much cheaper than a welfare & charity system large enough to accommodate everybody.
So that's what it's supposed to accomplish. By removing pockets of poverty in society, it just makes everything.. better. You know what happens to run down parts of town. Properties aren't maintained, people turn to crime for money, and so on. Crime will always be appealing, and sitting on your butt as well, to some people, but basic income is about scaling. It's not about individual people, it's about society as a whole. On such a large scale, the promise is that it's supposed to work very well and give you many benefits, without really putting a much larger burden on anyone at all, than what it is done now. In theory it should reduce healthcare costs, welfare costs, police costs, and many other costs we have in society that in some part are related to poverty and the things that come with it. That's why it's not a stupid idea, you actually might be able to get more out of it than the money you put in, without really affecting anyone in society in a negative way.