(Wow... an old-unanswered thread. Hope this would help anyone come across here)
1 & 2) I guess your problem is SQL Server's ODBC native client driver. SQL Server 2008 comes SQL Native Client 10.0 (unfortunately Microsoft doesn't provide stand alone installer for that). I see lots of VFP apps that 'hard code' the driver name inside the program and there's no way to change it (other than recompile the apps). By installing SQL Server, you install the ODBC driver, and that explains why the application run. Without SQL Server, the driver is not exist and that's why you got the error.
3) Try to install SQL Server Native Client 10.0 driver. You will need to 'trick' SQL Server installer a bit though. Information to do that is in http://technet.microsoft.com/en-us/library/ms131321%28v=sql.105%29
Hope this helps