The last FM thread was 5 or 6 pages long. The modulation is these simple circuits exploit the depleation capacitance in the transistor's B-C junction, which is essentially a reversed biased diode, not unlike those circuits that use an additional diode for modulation. These reversed biased diodes have a characteristic capacitance, the value of which is modulated by the reverse voltage, which is in turn modulated by the modulating signal. The modulator itself has very little voltage gain due to the fact that the collector's impeadance is very low at the lower modulating frequency. Thus, the signal is nearly all frequency modulated. In the O/P's circuit, the frequency determining components are C5, C6, L1 and the voltage dependent capacitance of Q2's B-E junction. If this network has high enough Q, then it should oscillate. That's why you want to make your own coils. BTW, one of the determanents of the coil's Q is it's resistance. You should use at least 1mm wire. You can go bigger, don't go smaller. Wind the max number of loops. You can trim some off later for tuning. Much messier to try to put them on.
To the O/P: just keep asking your questions and ignor all the noise. That's what this forum is for.
PS: I poked around and found a cleaner design ( see insert ) This one has all the component values specified, and shows a simple way to connect the antenna. Others will say it isn't worth building, but it shoud be fine for a first transmitter. You can get it working and add the other stuff later.