It would not be entrapment in the kid came to the FBI wanting to blow something up. It would be entrapment if the FBI went to the kid.
If someone was seeking a hit man, then they had the intention of committing a crime. But if you went to someone and offered it without solicitation, it would be entrapment.
Concur, but the initial solicitation does not have to be to the police. If someone is overheard talking about their desire to have someone killed and find a hitman to do it, then its not entrapment to provide one.