1. Probably maybe not rubbish either.

but I checked on baudrate from 300 to 250000. on 4800 there was nothing quiet on others rubbish.
2. I have 2 circuits assembled: 1 on a contact board the other on a universal board.
On the universal board it looks like this:
3. I was also hoping that these times were changing with the battery and the thing was clarifying, but in further experimentation everything was back to normal to those 30 seconds or so and on the two boards.
4. My 3.3V power supply on the board with the ESP 8266 is 0.5A (may not be enough) and the contact board is AMS 1117 3.3 (1A).
5. New approaches:
(a) I gave power to the ESP on the universal board from the power module (photo : alternative power supply) 3.3V - WDT reset time every 30 seconds
b) I gave power to the ESP on the universal board from 2 AA batteries (3.19V) - WDT reset time every 30 seconds or so
6. It's a pity that I don't have a test (laboratory ) power supply so that I could find out if this is the power supply - you can see from this that I need to buy one in the future. But from these experiments it seems that probably not asilization?
7. I still have an ESP8266 -03 module, but it's without goldpins and with a raster of 2mm, I'm afraid to solder such small ones - and I have a hm... transformer soldering iron, and when I have an IC I usually mount it on a socket, so as not to damage it.