Pixel-editor... I guess you mean something vaguely kin to MSpaint?
You can make a simple painting canvas with java.awt.Canvas and java.awt.event.MouseListener, never tried it myself, but I recall that there's a demo applet with the SDK that does this.
How familiar are you with Java and the standard libraries? You can do quite a bit with the standard libraries.
There're classes under java.awt.image that allow programmatic image manipulation (array-of-pixels access). Never used it myself, but you might want to give it a look.
There's java.io for file I/O and some java.io.File allows some file operations (creating, deleting, renaming, etc.). Haven't made heavy use of the File class, but the basics are to use a FIleInputStream or FileOutputStream with a Reader or Writer. Look at the API doc, or I can give you a quick code sample.
java.net has sockets an so on for network programs, nothing you'd need for your project, unless you're making an applet, then you might need java.net.URL
java.util has a bunch of odds and ends, including the Collections classes (List, HashTable, etc., etc.) and an RNG implementation.
java.awt contains the basic GUI framework, there's also javax.swing, which I haven't used much myself, but it provides similar functionality.
lookit all that rambling... hope it helps