I understand that an amplifier needs an inductor and a capacitor in a resonant circuit to build the output waveform without distortion. But why are there 2 inductors over the collector of the transistor and another inductor L2 near the output.
This should explain your questions: -
I was clearly wrong about C5 - upon further inspection it has nothing to do with being part of a tank circuit so apologies for that. And L1 is therefore not a tank inductor but just a collector load of about 240 ohms at midband broadcast FM frequencies.
Here's another attempt to fix my earlier stupidity: -