Break Override System Malfunction

I know several similar topics already exists, but I've decided to provide larger script. Maybe it will be helpful.

History (but possibly not related at all):
A car from the USA (Texas), Mazda CX-5 2018 2.5 NO I-Stop (2nd generation), with damage to the front end, was repaired and traveled around Ukraine for more than a year. No issues.
Car has windshield and front grille sensors and camera.
A second security system has been installed.
Car battery had a low life, so I've repaired it with an impulse battery charger.
What else.. I was told on Mazda service a year ago that chain tensioner should be better replaced (I didn't do this)
Also I've changed brake pads a year ago.

The story:
One cold snowy winter day, I noticed that the car would not turn off the engine. After some manipulations with P-R-D-P and Handbrake (electronic, btw) it stopped.
Sometimes gear shifter would not move to Parking.
Something seemed to be clicking in the area of ​​the gear shifter, and indicator in start/stop button a bit blinking. But after I've turned off 2nd Security System Tag it stopped, I think.

Errors (Warnings) appeared and almost always there:
- SBS Malfunction
- DRSS Malfunction
- DSC Malfunction
- SCBS Malfunction
Sometimes also with:
- Engine System Malfunction
- HBC/LAS System Malfunction
- Smart Brake System Malfunction

Also I've changed and later turned off 2nd Security System Tag battery.
Also turned off car battery for 15+ minutes.
Errors appeared again after drive (after 15-20 minutes, but could not disappear at all for some time).

Also first time I've noticed that stop lights blinking. Like alarm lights blinking, but that was definitely a stop lights.
Blink-Pause-Blink-Pause...
Turning off/on TCS helped. It happened few times.

In the service/dealer we replaced: BRAKE PEDAL STOP TAIL

Then Brake Override System Malfunction appeared as well. (maybe not related to replacement)
Start/stop button blinking orange while driving.

I know I need to take it to the service/dealer, but they doesn't know where to start searching. What would you advice?

Some examples:

 

1st step is to scan it for fault codes.

 

Service man scanned but found nothing special. Most of codes will be same as errors in example.