In the previous FM receiver, how does the left transistor amplify the input radio signal from the antenna at the collector and output it at the base, from what i know the base always has a smaller current than the collector.
With this common collector oscillator, the short answer is it lowers the parts count. That is why the output is not on the emitter.
RF amplifiers used for receiving are typically common base (or some call them grounded base amps). I don't see a real rf amp, just an osc/detector circuit.
This thing at first glance looks like an AM Radio (but its FM), because I don't see in the circuit where the typical phase discrimination or quadrature detector circuit.
The detection is a product of the collector-base junction and the base emitter junctions. That is why the base is the output.