How do I properly use the WiFi capabilities of ESP8266?
The following may not solve of your problems, but just in case it helps...
I was using the ESP8266 both in Station mode and AP. Both worked.
In AP mode, it worked but the ESP8266 ignored my instructions to set name and password for the AP , until I realised the following
. The password must at least be 8 characters long, otherwise the instruction is ignored
. in the IDE, you should erase flash AND WiFI settings, otherwise it will be "lazy" and use previous settings