Hi Oswald,
this very much sounds like you either need to calibrate your ESCs and/or set up the min,neutral,max properly in your servo section.
The neutral value should be the pulse length in us at which your ESCs turn the motors on, but at an acceptable idle speed. Min is off in that case and max is well, max...
This has nothing to do with the gains or anything like that at this point... first you need to make sure that if you send the "neutral" value all motors will rotate at idle speed and reach their maximum speed at max and not before.
I never use rate mode, but the ahrs (attitude estimation) should run as normal... and works as expected here...
Can you provide some more details?
Cheers, Felix