But unlike his mother, no other adult is required to act in the child’s interest?
I’d say “parent or guardian”, not just mother, but otherwise yes.
If the mother fails to act in the child’s best interest, and if no one takes custody of the child to do so, it will die from neglect.
Yes, it is sort of imaginable, but I don’t think it has any real likelihood of happening. The only possibility for that would be abandonment of a child who cannot present himself to others, for example an infant or a small child living in a mountain cabin 50 miles from the nearest person.
If the government should not be able to compel society to prevent this, what difference does it make then if I sell it explosives and it blows itself up?
Remember that at the core, children have no legal right to buy anything. An exception is made for harmless stuff, but not for harmful stuff. The difference is two-fold. First, the child must be prevented from initiating force against others, and it is highly unlikely that a child would acquire explosives for a rights-respecting purpose. Second, basic benevolence would allow (and not obligate) a kindly old lady to adopt an orphan or abandoned child and serve as the custodian of the rights of the child, when necessary restricting his actions to protect his life. It would also allow (but not compel) the government to objectively characterize certain cases of extreme harm to the child and state that people may not directly or indirectly inflict that level of harm on the child. That would include (non-exhaustively) torturing a child, enslaving a child, having sex with a child and providing a child with explosives or deadly toxins.