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I Don't know. Try some of the textfield's methods and see what they do.

If you want other methods to have access to it, it needs to be defined at the class level (outside of a method).

They need action listeners added to them so something can be done when they are pressed.

What is a JTextView?

If its a class, read its API doc to see what methods it has that will do what you want.

It is not allowed to add a window to a container.
It is allowed to add just about any other component to a container.

Use a JPanel NOT a JFrame.

Where is the JPanel with the gridlayout that is supposed to hold the buttons?
That when filled is added to the center of the borderlayout

Use different layout managers and JPanels that hold some of the components with its own layout manager.
With a borderlayout put a large component in North and a JPanel with a gridlayout in center...

Yes, there are many different layout managers.
Did you look at the link in post#2?

Where is it set for the dep JFrame?

Which button is shown? The first one added or the last one?

What layout manager is controlling the layout for the container that the buttons are being added to?

That is a call to the class's constructor. See the tutorial on how to write class constructors:
Providing Constructors for Your Classes (The Java™ Tutorials > Learning the Java Language > Classes...

Where is the constructor for the class?
Where is the method: gui() called? Did you mean for the gui() method to be coded as a constructor?

Why are there two JFrames? One is extended the other is...

Please explain what is wrong.

Take a look at the tutorial about how to use layout managers:
http://docs.oracle.com/javase/tutorial/uiswing/layout/index.html