Shared/Common Controller Code:
What you've described is a "Component":
Components are packages of logic that are shared between controllers.
If you find yourself wanting to copy and paste things between
controllers, you might consider wrapping some functionality in a
component.
See: http://book.cakephp.org/2.0/en/controllers/components.html
Shared/Common View Code:
As far as the View is concerned, there are a few options. If you want the entire view, you can just specify which view to render: $this->render('TestView/index');
Or, if you want a small chunk of code, you can try an Element.
All together:
If you find yourself creating a lot of the different "parts" (View, Controller/Component, Model/Behavior)...etc, all for the same general purposes (ie cropping a photo), you could think about creating a Plugin.
Side note:
Side note: Usually, I've heard the functions in Controllers referred to as "actions", and the functions in Models called "methods". They're all really methods (a function within a class/object), but - that's how they're commonly referred to.