So, if I understand your question correctly, the camera, its drivers and the application that grabs and stores images from it are to run on the Linux host, but users that access the camera application will be using Windows. You want to know how to control and log data from the linux hosted camera application through a Windows user interface.
If this is a correct summary, then I would suggest the following: run an X server (see list at http://www.rahul.net/kenton/xsites.html#XMicrosoft
) and SSH client on your Windows system(s), and simply access the Linux host application that way. Then you only have to develop code on one platform, and any client with X can access it. This also solves your authentication problem, by using the existing and well known SSH/SSL system.
Alternatively, you will have to write a client-server application, where the server runs on the Linux host, and the client runs on the Windows hosts. This is probably best done using TCP or UDP to pass messages between the host applications. Your application can be free to define whatever protocol you wish to devise for this purpose. I don't think you provided enough detail for anyone to give a very detailed reply.
A good online C tutorial with a somewhat Unix/Linux angle is http://www.cs.cf.ac.uk/Dave/C/