I want to know how to write a C# desktop application that can connect to the mobile version of the same application (that I will create). The desktop application will be used as a backup/restore for the mobile application.
I want to know also how to write the mobile version (using C# if possible).
From your other posts, it appears you are trying to write a Symbian 7 application to sync a proprietary data format with a custom Windows 7 desktop application. That is critical information to leave out of your question; let me know if I am mistaken.
If that is correct, you have set a difficult task; Symbian 7 is an extremely old OS, I do not know if the Carbide C++ IDE can develop apps for it. If not, you are looking for old versions of commercial AppForge or Metrowerks compilers, you may be able to track these down at the Symbian Foundation.
Then the hard work starts; Symbian is an extremely difficult platform to develop on, and information on old pre-Symbian 9 OSes is scarce. If you are not already an expert on Symbian, I suggest hiring a contractor with previous Symbian 7 experience.
The hard work does not end there, Bluetooth is also notoriously difficult to develop for. The spec is incomplete, and most manufacturers only partially implement it in undocumented ways. One Bluetooth team I know of spent more time debugging hardware problems than developing the software.
This is only the start; you still have to define the Bluetooth data and synchronization protocols; I do not know if ActiveSync was ever supported on Symbian 7, so you are starting from a blank page here. Then you have to develop the Windows app.
You are looking at an enormous commitment to develop on ancient and unsupported hardware. I suggest investigating more modern and capable hardware.