How are you accessing the database with FMGO? If it is stored local on the device ODBC won't work. I beleive if you share the database from the computer with FM Pro and access the database this way your ODBC should work. Don't quote me on either of the privous statments as I have not tried it myself.
Personally I stay away from Filemaker when using something like MySQL and develop using php for web or any number of other options for the desktop.
Yes, turn on the share and open port 5003 to your machine.