I read the autotune page (copter.ardupilot.com/wiki/autotune/) and I don’t understand something. It says that autotune will engage in stabilize mode. So does that mean if I am in altitude hold and then switch on Autotune, then the copter will go in stabilize mode? If so, isn’t that dangerous (for example, the throttle at which my copter hovers is around 1350…)?
No, it’s a warning that autotune can be activated even when you are in stabilise and to be careful you do not accidently activate autotune while in stabilise mode.
If you are in alt hold (as you are supposed to be) activating auto tune the apm/pixhawk will remain in alt hold until you change the flight mode.