1,2) I was able to connect to a MySQL Database using your same version of the MyODBC Driver and the SQL Toolkit in LabWindows. After I setup a System DSN for the database, connecting to the database went smoothly. I assume the DBBind... functions should work without any additional setup.
3) It looks to me like the C API for MySQL was designed specifically for a UNIX system, or Visual C++. It appears that several Windows libraries and headers would need to be included in the project in order to get the API to work with LabWindows. I bet that these libraries could be made to work with LabWindows, but it might involve some changes to the MySQL header files.
Good Luck!