Have you tried setting the web editor's baud rate to both the old and the new values? I ask because the CIOBAUD command has been obsolete for a while now so, depending on the age of your device, it may have done nothing. The command was replaced by "AT+UART_CUR" and "AT+UART_DEF" which have a different syntax.
See this answer to a similar question.
Yes, here's an example:
// Declare a serial object to talk to ESP8266
SoftwareSerial EspSerial(WIFITX_PIN, WIFIRX_PIN); // RX, TX
// Init WiFi serial
I've used 9600 baud in my example since SoftwareSerial may not work well at faster speeds.
Is it possible to send AT commands from the code instead of the
Yes, easily. Once the above code has run (and note that I've deleted an unnecessary line since update 1), you can send strings to the ESP with EspSerial.print() and EspSerial.println(). Here's an AT command example:
// Set 9600 baud, standard 8-bit frame, and save as power-on default: