Hello. I have code very similar to what you are looking for. It's currently running on a remote hydroponic system that sends me data from environmental sensors and allows me to control relays via SMS.
The system sends data via SMS to a phone number that is stored in the Arduino EEPROM. The system can also be sent a contact number via SMS. This number is saved in EEPROM and used for subsequent communications. I.e. you can remotely change the phone number the unit contacts.
Writing data to MySQL over GPRS will not be a problem. I'll need the server, database and login data. I think the best approach would be to write a short PHP program that the Arduino hits and sends data to. The PHP would then login to the database and push the sent data to it.
Shutting down the FONA when not in use is no problem.
Changing the Arduino's environment upon receiving SMS messages is already in my code. I'll need to know what control settings you will want to change.
I have all necessary software and hardware except that my FONA is an 800, rather than an 808. The code to grab GPS data from an 808 is straight-forward and available from Adafruit. I can plug it into the sketch and let you test it or I can order an 808 and test it here. I would prefer the first case, as I already have 2 FONAs, but I can buy one if absolutely necessary.
I also have DHT temp/humidity sensors, thermistors and a stand-alone digital humidity sensor. I can setup test cases using any of these if you like.