Easiest question first, yes, you get to say what your preference is for age. And if you set yourself up for a particular age, you are well within your rights to turn down children of a different age. If you have all baby and toddler stuff, you can turn down a teenager.
In reality, you may be offered children out of your preferred age rang and choose to take them, sometimes.
Money... it varies. We get an "allowance" to cover "expenses" - in practice that means, a non destructive child with a normal diet and able to walk to the bus stop - we make a profit.. very destructive child, expensive diet, needs taxis, we will make a loss.
But you can choose who you foster for, I am LA, but some fostering agencies offer a far higher rate of pay
Are children "mean"? yes, but I don't really see it in those terms Do we have children with absolutely no idea how to behave, no boundaries, no empathy, yes, because they have not been taught. Do children steal, yes, we have been burgled by a child who snuck back after leaving us. When the child is with us, no, not generally, because I supervise them