Why is my Android phone behaving strangely?

Question

Android

Good afternoon, the phone behaves strangely, it can turn on Google search and write various queries, here are examples of "hehe", ")))". It also switches between windows, turns on wi-fi, gps, if the phone is turned off, it can turn itself on. He referred to a virus, formatted the phone, but after a while everything started all over again, and I noticed a strange wi-fi network in the saved ones, the name of which was written in hexadecimal number system. I decided to reflash, put custom firmware through the recovery, and the phone worked, but as soon as I connected to the Internet, everything happened again.
What can be wrong?

Answer 1

...they are everywhere...

Answer 2

If the actions are very chaotic, and not purposeful - I would sin on the sensor, or a small distance from the display to it and the heat of the display causes this, or another flaw.