image processing

1. I don't know what you mean by copy, but you can process parts of images. There are methods defined in the Graphics2D class for dealing with parts of images, or you can access the raw pixel data like an array.
2. From java you can execute external applications (if you have an application that has a command line interface) or you can write dll's for working with other programs (but you will probably find this very difficult).
3. A java application can act like a server or a client. You have the ServerSocket class for servers and the Socket class for clients. You can send/receive any kind of data over tcp/ip (just like you would do in c++).