@Michail71
Ok, the default system is truly and mightily messed up! 
You might want to just sit on the ground and watch what happens with the AP as you turn it on/off while on the ground.
I sat on the ground at KSAR (just a plain airport I test short stuff out of) which is about 540MSL. I set my heading bug to the runway heading, and set in a desired altitude of 3500’ MSL, with a VS of 500 FPM and verified trim was set right at takeoff. As soon as I turned the AP on, the trim started moving up on the indicator (nose down). By the time I got everything set, the trim had set itself to full nose down. After I turned the AP off, the trim stayed at full nose down…not a good thing! LOL
I could manually move the trim to T/O, and then when I was in the air I turned the AP back on, and watched the trim once again go full nose down.
There were several other really odd things that happened too, but basically that AP is just bad. I’d consider looking at the thread for the mod, and see if you’d rather use that (which by all accounts is much better).
Even the default C-172 G1000 version AP works much better than the steam gauge version of that plane.
So without being able to share a cockpit (hopefully someday!), it appears all or most of the issues are caused by the default AP, and not something you’re doing!
Regards
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