Yes, this is possible. Here is some example code
to get you started. You should probably work with the newer Gtk+ (2.x) series.
As far as right-clicking to create a popup, you can modify the .glade file with the Glade UI designer. Connect the proper event to the callback you specify on the widget you specify. Right-clicks can be detected by using the proper mask
I would also highly recommend The Official GNOME 2 Developer's Guide
. It's got tons of info on Gtk+.