That transmitter circuit is just a simple oscillator, not a very good one at that, with a random piece of wire tapped onto the frequency determining tuned circuit.
The modulation applied to the base of the transistor is not well defined.
(I will leave it to Audioguru to explain how bad the audio frequency response will be).
The output impedance of the transistor will be quite low, however any load you apply to this circuit will damp the tuned circuit, eventually killing the RF oscillations.
The impedance of your antenna cannot be considered in isolation, if it is just a "small aluminium rod" it needs some kind of groundplane to work against, you are probably just using the mass of the rest of the circuit, the antenna feed impedance will be totally undefined.
Accurate analysis of this circuit is just about impossible, its operation is very depandant on stray capacitance and inductance which cannot be defined without knowing the exact physical construction.
JimB