The quiz on the phone is confusing, because I think the questioner is mixing up two different kinds of telephones. If you are talking about a desktop phone, then cradle is correct about where you place the handset. The buttons that you would tap? (Actually, not tap. You would press them briefly, say for a few seconds, then release them, to see if the dial tone returns.) I have no idea, they're just "buttons". They operate the switches that enable/disable the phone operation, and likely the phone co. engineers had a name for them, but I don;t know it.

Now-- if you have a wall-mounted phone (or a phone booth phone, which is also a wall-mount design), then the thing you press and release is indeed called a hook, because it looks like one. The handset hangs on it, it isn't "cradled" like on a desktop phone. The hook operates the same internal switches as a button set would.