Is this circuit using a hartely osc.?
Yes, because its coil is tapped and provides positive feedback to the base of the transistor.
1- is the emitter resistor affect the frequency of oscillation?
No, it affects the current in the transistor which changes the output power.
2- this is a transmitter circuit, is it FM or AM and why?
It is simply a continuous carrier frequency without AM nor FM modulation.
If something modulates the amplitude of the carrier then it is AM. If something modulates the frequency of the carrier then it is FM. Some simple modulators produce both at the same time.