So this could be used to describe both the act of initiating a phone conversation (calling someone) as well as the act of holding the conversation itself (being on the phone)? In English I have only ever heard the equivalent verb "telephone" (or its shortened form "phone") describe the former (and then, at least in the US, only rarely; as "call" is tremendously more common). Seems like Hungarian is more versatile!
Another way "to call somebody" is "felhívni valakit". But it does need a direct object.
That would be understood in English, but it isn't normal. The given translation ("the boy is on the phone") is much better.