I've made a little video explaining my problems, it looked like the most direct way of explaining them to me.
In short, apart from the fact that i had my pusher and normal prop inverted (and thus i wasn't able to lift), with the throttle lowered at the minimum spinning speed, some of the props are stopped. Trying to tilt the copter doesn't create a behaviour that makes sense to me. The accelerometer of the APM is perfectly calibrated (and i can see it from the flight data panel).
(i've tried to run the motor test utility via CLI, but it doesn't seem to do nothing and the command returns a blank after about one minute)
Any suggestion is welcome. Thanks.