I'm not wrong about the Bill of Rights. The Bill of Rights defined a set of rights protected explicitly and then the 9th and 10th Amendments, part of the Bill of Rights, basically said what you said - that rights exist beyond those identified explicitly and that those were protected just as much as those listed. That's why there was so much debate over whether or not there should even be such a thing.
Many felt that having a bill of rights would later be interpreted that things not listed would not be protected; government would claim that only those rights listed are protected. And they were right; there are many who suggest the government can do something because it isn't explicitly protected in the Constitution. On the other side, there were those who felt that if there was no bill of rights, the government would claim the authority to control things not intended for it to control. And they were right. Imagine gun rights today if there was no 2nd Amendment. How many are claiming that your phone is not protected or your online activity? So, both sides of that debate were right; both recognized that government would feed itself.
As for the gun side of your argument, if there were laws against children owning guns, share them. The argument has been made, even wrongly upheld in the Supreme Court, that children do not have constitutional rights. Similarly, many, especially self-proclaimed conservatives, argue that non-citizens and especially illegal aliens don't have constitutional rights. But the government only has the power granted in the Constitution so where would they have any power at all to have any interaction with an illegal alien? The government has the power that is in the Constitution, period. It doesn't matter where in the world or with anyone from anywhere in the world, the Constitution is the same. Whether a person is child or adult, white or black, citizen or illegal alien, the right to keep and bear arms shall not be infringed.
Parents, on the other hand, are not limited by the Constitution and they are the ones who can choose whether or not to allow their children to have guns.
As for your other argument, about shooting recklessly, shooting is not protected by the Constitution. There are rights, as you suggest, that are not included in the Constitution and the right to shoot your gun in defense of life, or perhaps for property, would fit in the 9th and 10th Amendments. Shooting recklessly, though, is not a right.
And not exactly in response to your post but related to the topic, if the 2nd Amendment were repealed, the right to keep and bear arms would still be protected by the 9th and 10th Amendments. If those were repealed, the right to keep and bear arms would always be a right, an inalienable right, and government cannot take that away. They can punish a person and use force and threat of force to prevent exercise of the right but the right remains...