Aloha khan,

     With the P3, the IMU calibration works wonders and the P4 has two IMU units for more precise data.  Each of the problems could be related to a need to calibrate the IMUs.

     You did not mention that you did a controller calibration.  Your sticks could be way off and cause the same problems.  The IMU, gimbal and controller can each contribute to the problems you mention, so it is best to calibrate each one.  Be sure to calibrate your compass while you are at it.  I think that is all of them?  Good Luck, I am sure you are anxious to get airborne!

Aloha and Drone On!

wrathofkhan,
There is no such a special method of calibration but there are some tricks like "cold calibration" when you put your drone into the fridge for 20 min ( without battery)  and calibrate the IMU after.
It can add a little bit more precision into your work.
To solve the issue with horizon you also need to calibrate the gimbal and RC.

What's the procedure for calibrating the RC?
[EDIT]Never mind I found it in the DJI Go app[/EDIT]