Mars sonic boom

I wonder if Mars Atmosphere is thick enough for flying anything...
I've read around that Nasa is thinking at something flying in the mars atmosphere.
Well, I wonder:
1) Is it possible to fly something in the Martian atmosphere just in the same way we do on earth? If so, I think the phisical properties of that "atmosphere" are hard to simulate here, so HOW are they trying with?
2) Let's imagine we can fly something. I can suppose the "propellers" needed HAVE TO BE bigger than Earth's one since the lower density: but how much bigger?
3) if an atmosphere "enough for flying" do exist, what's the relative sonic boom speed (if any) up there?
4) Maybe would be interesting to send a lander up there, capable of generating a "known spectra sound" or selectable frequencies; and trying to record the resulting sound using a suitable microphone. Beaming the recorded result back to earth, just we already do with light and the changing color filters on the pancams...
Maybe would be interesting to have a better knowledge on the Mars atmosphere mixture, the density and the chemical/phisical properties.