I almost held back about this, but marv said burn the mother down, so...
Ahh, the Fourth and Fifth Amendments, citadels against an overbearing police state, and a source of constantly shifting legal mumbo jumbo. There are only a few bright lines in arrest and miranda jurisprudence, such as: if they have handcuffs on, they are considered "in custody". Importantly "arrest" rules fall under the "seizure" portion of the Fourth Amendment, and "miranda" rules fall under the "due process" portion of the Fifth. Highly related, but still get different analysis. You can be arrested and not questioned, and miranda probably won't come up. You can be questioned without being arrested, this happens a LOT. You can be stopped for questioning without being either.
The thing Marv is saying is correct: the cops can ask all kinds of questions, and intimidate the shit out of the kid, all they want, but any info they get cannot be used against him later (including info they get while following leads based on his statements) if they didn't give miranda warnings; many jurisdictions also require parents be given the option of being present.
OJ's point is also essentially correct: the situation as you describe it is one that almost any court will determine counted as "custodial questioning" and will throw out any statements.
Important clarifications: it is not "illegal" for police to conduct custodial interviews without giving miranda, they just don't get to use the info; "arrest" is not the issue when figuring out when to give miranda, there must be "custody" and "questioning/interview/interrogation"; "custody" is a question of whether a "reasonable person" would feel free to leave in the same situation; "questioning" matters because spontaneous statements are freebies.
All that said, the number of court decisions that are at odds with each other in this territory is immense. I have a hand out somewhere with columns of "not miranda" and "miranda" each containing almost identical circumstances with case citations to the appellate court that made the determination. The same goes for what constitutes invoking miranda, such as saying "I don't want to answer questions anymore" or "I want a lawyer now". It is HIGHLY subjective based on case circumstances. All of these tests, before a court, are called "totality of the circumstances" tests, which is a fancy way of saying "the court can almost always do what it wants, as long as it finds something unique about this set of facts, and explains nominally how it matters."
The cops SHOULD have read the kid miranda if they wanted to use any of the info against him, but they might also have thought "we don't care, we needed the info for safety more than we cared about prosecuting him."
EDIT: Aliki!
