Need help understanding simple FM transmitter
Resonant frequency formula is nearly correct. You have mostly one L - stray inductance is not included. But you have four capacitances that can be assumed in parallel:

C2 (obviously)

C3 (it is actually combined with \$ C_{be} \$ of the transistor)

\$ C_{bc} \$ of the transistor

Antenna reactance, which is often capacitive.
\$ F_r= \frac {1}{2 \pi \sqrt {L(C_2 + C_3 + C_{bc} + C_{ant})}}\$


Again, stray capacitance hasn't been included - it will cause \$F_r \$ to be even lower. Because L's and C's are so small, using this formula to hit a desired frequency is very difficult.
This is an oscillator whose amplitude doesn't decay, but grows until non-linear losses limit the amplitude. C4 is the element that mostly causes positive feedback - making this transistor oscillate.
C1 is a &quot;bypass&quot; capacitor that grounds the transistor base at the oscillating frequency, but allows low-frequency audio to change base voltage. At audio frequencies, reactance of C1 is mostly insignificant.
Everybody wants more range. Making R2 too small will kill the oscillations. Power output might increase, but you'll hardly notice range improvement. A power amplifier would improve power, but would likely violate FCC rules (in America). 
Using SPICE to see the FM modulation would be extremely tedious. You must use a transient analysis with time-step small enough to have many steps at the oscillating frequency (about 100 MHz). Yet the simulation must run for milliseconds.