These are some BIG questions in a very small package.
A Factory Method is described in the GoF (Gang of Four) book. The method takes some parameters and returns an interface (or abstract class). The idea is that depending on the data that is passed in, objects of different class types are returned, although they must all implement the interface (or inherit the abstract class).
Light Weight Components: AWT is an example of heavy weight components - each AWT component is reliant on the underlying operating system for implementation. Swing is an example of lightweight components - each Swing component is made out of basic paint routines and events within
Java and does not depend on the underlying operating system to specifically implement this component.
A Decorator Class (GoF) will provide the same interface as the class that is being decorated, but it will usually add some enhancement. A decorator class usually does not inherit what it decorates, rather, it contains what it decorates.
Functor is new to me, but I found a reference in the GoF book. Something about "objects that are functions". Apparently some guy named "Coplien" thought it up.