ESP 12F does not return OK on AT
I have resolved the problem myself. The small ESP 12F module did not have pull-up resistor on EN pin and pull-down on GPIO15. Despite the fact that AI-Thinker DOES have the resistors in their ESP 12F datasheet schematics. I have added resistors and board started to work. For others, I have set up baud rate of serial monitor to 74880 and reset method to ck, I reset manually when IDE is waiting to upload. Also when programming, the GPIO0 needs to be pulled down. When you reset the chip you get response on serial terminal that contains boot mode:(x,y). x are bits of GPIO15, GPIO0 and GPIO2, If you get value of x 3 or more it means you need to pull GPIO15 and GPIO0 low. For flashing then there should be boot mode:(1,y), for running the sketch boot mode:(3,y). I do not know what y means but it seems it does not matter.

I also encountered another strange behavior. I use OTA from web server and sometimes the ESP just did not connect to web server and indstead expected http code 200 it returned code 400. After long debugging it turned out that I have multiple SSID at home provided by ZYXEL router, some with password and some without it. When I was connected to SSID with password, the server was still returning http code 400. When I connected to other SSID without password, server connection was OK, server returned code 200 and OTA proceeded without problems.