Sara,
First you must be very clear about RF operating frequency ranges...
SUB-GHZ, GSM, CDMA, ZIGBEE all operates at different frequency...
Zigbee has no connection with GSM...As zigbee is 2.4GHz and GSM - 900/1800 MHz....
First of all, get hands on experience of the GSM using PIC Controller...
For example, in the PIC use UART interrupt to capture the responses given by the GSM module...
Validate the responses in your MAIN() function inside while(1) loop...
May be you can try few things as said below:
1. Do not send any command to the GSM module until you get CALL READY in the UART...
2. Try sending SMS using your controller.
3. Try to activate GPRS and get the IP for data transfer.
4. Try TCP IP data transfer making your GSM as SERVER by putting it in SERVER LISTENING MODE...There is a TCP TEST TOOL software where you can test this...
5. Similarly write codings to read the SMS from the GSM module and take action accordingly if warranted or delete the sms using your controller...
You can try it out and see yourself...