hi,
I dont know how C works but it seems that at:
unsigned char ATEO[] = "ATEO";
unsigned char Delete[] = "AT+CMGD=1"; //Deleteing SMS in index 1
and after the AT+CMGD=1 you need to send a CR (carriage Return) instruction to the phone.
Also make sure you can read data from phone, maybe there is a connection problem, hardware.
I mean, you may send commands but the phone could not read them because of special RS232 connection needs.
Also, about hardware, On your Ericsson serial cable, on the site of the 9-pin RS232 you may need to set to logic level 1 (high) the pin number 4. On my R320 and T65 works with this setting, otherwise the phone cannot communicate serially with the microcontroller. I dont remember on the phone's site what pin 4 is but I thing is a control signal like CTS/RTS or simillar.
I hope I help a little.