With reference to this schematic:

http://www.pyroelectro.com/projects/pyro_rf_transmitter_27mhz/img/schematic.png
I'd like to know if there is a general rule of thumb for determining the

antenna impedance Z(w) and therefore the matching inductance L3.

A vertical 12 inch piece of #28AWG wire, over ground, at 27MHz, will look

something like 0.3 ohms radiation resistance, in series with about 2.5pF.

Required series inductance will be 13.92uH.

Radiotron Designer's Handbook, Chapter 22, Section iii gives:

-jZo cot(2*pi*L/lambda) for the reactive component, where:

Zo=138 log(lambda/d) - 104 ohms, where d = wire diameter.

I do it on a spreadsheet I adapted from an HP41 calculator library program.

Also, I'd like to know what is the meaning behind the choice of the "12

inches of AWG 28" (cause 12inches do not seem to me like any fraction of

the wavelength lambda).

Just a convenient piece of wire? No other reason I can see. #28 wire won't

self-support very well, anyway.

A quick and dirty simulation using the above antenna model shows resonance

at about 28.37MHz, with your published component values. Probably not much

radiation from the "antenna" at 27MHz.