messagingtoolkit

1)Does it come with vb.net/C# source code explaining how to send and receive SMS using GSM modem and android phone ?

Yes. You can download the installer and the sample program and source code are available.

2) Does my windows application running on the desktop connect to android using Bluetooth or USB for sending/receiving SMS ?

Connection to Android is through HTTP protocol through REST
Connection to GSM modem is through serial port/USB or Bluetooth port

3) Can I send a picture saved on c:\ as mms using your toolkit ?

You can send the MMS through GSM modem.

The Android app exposes REST API to send MMS as well.

This is something I have been looking for a while.