You are trying to make the original old FM transmitter that usually does not work, I fixed it 13 years ago.
1) Its audio preamp transistor is saturated if the battery is brand new and the hFE of the transistor is high and the transistor is cutoff if the battery is running down and the hFE of the transistor is low. I added a I added a low dropout voltage regulator to fix it.
2) The radio frequency of the transmitter changes as the battery runs down so I connected the RF oscillator to the added voltage regulator.
3) The radio frequency changes when something moves towards or away from the antenna because the antenna connected directly to the oscillator tuned LC circuit. I added an RF amplifier between the oscillator and antenna to fix it.
4) The sounds from the transmitter heard on a normal FM radio were very muffled with no high audio frequencies. I reduced the value of C3 to 1/20th to 470pF and added pre-emphasis treble boost like all FM radio stations have.
I built mine on a planned and compact stripboard layout because the very high frequency will not work on a solderless breadboard with the high stray capacitances between the rows of contacts and the wires that are all over the place.
The leads of my expensive Fluke DMM measure 0.19nF which is 190pF. Without the leads it measures 0.16nF which is 160pF.
Here is my fixed FM transmitter: