The potentiometers that I used are 20 kilo ohms. Is it possible that they are the source of the problem?

 

Should I lower the resistance of the resistor?

Low enough would burn out the B/E junction.

It looks like there's a mistake in that schematic, but I'm not familiar with that type.

 

Is there a standard FM radio schematic like how there's a standard astable multi vibrator schematic or a standard full wave rectifier schematic?

 

Here is your circuit on a different site. Note the comment under 'Limitations'!

 

Is there a standard FM radio schematic like how there's a standard astable multi vibrator schematic or a standard full wave rectifier schematic?

No - in the early pioneering days, experimenters followed a "more or less" approach and moved components around for best results.

This produced some peculiar circuits that work surprisingly well - and a lot of people can't figure out why!