capacitors in FM transmitter circuit
C1 in parallel with the microphone will have two main effects:

It will reduce the high-frequency response at high audio frequencies. I'm not sure why that woul dbe desirable in the circuit
It will reduce the likelihood of picking up RF interference by the microphone whic could happen if it connected by a cable.

C4 also reduces the response of the circuit to high audio frequencies (although it seems too large for that purpose) C4 also acts as an RF ground for the base of the final oscillator stage.
C5 is to provide positive feedback in the final stage so it acts as an oscillator. L1 and C6 are the main tuning components with the circuit oscillating at the resonant frequency of L1/C6. C6 and the characteristics of the transistor will also affect the oscillating frequency.
The final stage is often referred to as a Colpitts oscillator.