I've seen this design before.
You can see two oscillators in there, identical. Their outputs are mixed together. If they are in tune then the mixing produces no audio or a very low tone, but if one is thrown out of tune - by the presence of metal near to its inductor - it'll shift in frequency, and their mix will produce a high tone. No radio required. There is a small 'fine adj' pot in there that lets you tune them initially, to compensate for the unavoidable variation in component values.
You can aubstitute any of the resistors or capacitors for a replacement of more-or-less the same value. 2k7, 3k, 4k, close enough. So long as the two oscillators match: Anything you change in one, you must change in the other too.
The right-hand side of the circuit is nothing but an audio amplifier, and so is very easy for you to replace with whatever output amplifier is most easily constructed from your available scrap components. Tear about any cheap-and-nasty set of powered speakers, there's an audio amplifier board inside just begging to be repurposed. The amplifier design shown in that circuit offers high voltage gain but little power output - it'll drive a pizo, but not a full-size speaker.