How do I clear a Panel?

Question 1

Start by taking a look at some of the panels that are involved...

NumberPanel, OperationPanel, WritingZone which are instance variables and emptyPane which is a final local variable.

Each of these will either need to be "cleared" or recreated.

A simple solution would be to have emptyPane as the only instance variable and simple call emptyPane.removeAll() each to the ActionListener is triggered, but as it stands, you're going to have to call removeAll on each of the fore-mentioned panels, for example...

public void actionPerformed(ActionEvent e) {
    emptyPanel.removeAll();
    NumberPanel.removeAll();
    OperationPanel.removeAll();
    WritingZone.setText(null);

Now, personally, I would start by creating a BasicCalculatorPane and an AdvancedCalculatorPane. Each containing the required UI elements and logic to make them work. Then when the user selects between them, remove what ever calculator pane is on the screen and create a new instance of the required calculator and add it. Equally, you could maintain a single instance of reach, but provide a "reset" option, which would allow you to reset the interface, but would save you from having to create more instances of these panels

Question 2

Try this

yourPanel.getContentPane().removeAll();//clean main screen Frame
yourPanel.add(newContent);//add the desire Panel
yourPanel.revalidate();

Question 3

Please try this

public class Calculator  extends JFrame implements ActionListener{

    /**
     * 
     */
    private static final long serialVersionUID = 1L;
    JPanel NumberPanel = new JPanel();
    String [] ButtonString = {"7","8","9","4","5","6","1","2","3","0",".","+/-"};
    JButton ButtonArray [] = new JButton[ButtonString.length];
    JPanel OperationPanel = new JPanel();
    String [] OperationString = {"Erase","Ac","*","/","+","-","Ans","="};
    JButton [] OperationArray = new JButton [OperationString.length];
    JTextField WritingZone = new JTextField(27);
    JButton b1 = new JButton("Ok");
    JButton b2 = new JButton("Exit");
    double first = 0;
    double second = 0;
    double result = 0;
    char operation = ' ';
    Calculator (){
        super("Project Wolverine");
        setLayout(new BorderLayout(5,5));
        JPanel radio1 = new JPanel();
        final JRadioButton r1 = new JRadioButton("Simple Calculator");
        final JRadioButton r2 = new JRadioButton("Advanced Calculator");
        ButtonGroup g1 = new ButtonGroup();
        g1.add(r1);
        g1.add(r2);
        radio1.setLayout(new GridLayout (3,1,5,5));
        radio1.add(r1);
        radio1.add(r2);
        radio1.setBorder(BorderFactory.createTitledBorder("Choose a calculator"));
        JPanel panel2 = new JPanel();
        panel2.setLayout(new GridLayout(1,2,5,5));
        panel2.add(b1);
        panel2.add(b2);
        radio1.add(panel2);
        add(BorderLayout.WEST, radio1);
        final JPanel emptyPanel = new JPanel();
        emptyPanel.setVisible(false);
        emptyPanel.setLayout(new FlowLayout());
        add(BorderLayout.EAST, emptyPanel);


        b1.addActionListener(new ActionListener(){
            public void actionPerformed(ActionEvent e){

                if (e.getSource()==b1){

                if (r1.isSelected()){
                    for (int a = 0 ; a < ButtonArray.length ; a++){
                        ButtonArray[a]= new JButton (ButtonString[a]);
                    }
                    NumberPanel.removeAll();
                    NumberPanel.setLayout(new GridLayout(4,3,5,5));
                    for (int a = 0 ; a < ButtonArray.length ; a++){
                        NumberPanel.add(ButtonArray[a]);
                    }

                    for (int a = 0 ; a < OperationArray.length ; a++){
                        OperationArray[a]= new JButton(OperationString[a]);
                    }
                    OperationPanel.removeAll();
                    OperationPanel.setLayout(new GridLayout(4,2,5,5));
                    for (int a = 0 ; a < OperationArray.length ; a++){
                        OperationPanel.add(OperationArray[a]);
                    }

                    JPanel Finalpanel = new JPanel();
                    Finalpanel.setLayout(new FlowLayout());
                    Finalpanel.add(NumberPanel);Finalpanel.add(OperationPanel);


                    WritingZone.setComponentOrientation(ComponentOrientation.RIGHT_TO_LEFT);
                    WritingZone.setBorder(BorderFactory.createLoweredSoftBevelBorder());
                    WritingZone.setEditable(false);
                    WritingZone.setBackground(Color.white);
                    JPanel TextPanel = new JPanel();
                    TextPanel.add(WritingZone);


                    for(int a = 0 ; a < ButtonArray.length; a++){
                        ButtonArray[a].addActionListener(new ActionListener(){
                            public void actionPerformed(ActionEvent e){
                                for (int a = 0; a < ButtonArray.length-1; a++){
                                    if(e.getSource()==ButtonArray[a]){
                                        String temp = WritingZone.getText();
                                        WritingZone.setText(temp+ButtonArray[a].getText());
                                    }
                                }
                           }
                        });
                    }
                    ButtonArray[11].addActionListener(new ActionListener(){
                        public void actionPerformed(ActionEvent e){
                            if(e.getSource()==ButtonArray[11]){
                                StringBuilder temp = new StringBuilder();
                                temp.append(WritingZone.getText());
                                WritingZone.setText("");
                                for (int a = 0; a < temp.length(); a++){
                                    if (temp.charAt(a)=='-'){
                                        temp.deleteCharAt(a);
                                        WritingZone.setText(temp.toString());
                                    }
                                    else{
                                        WritingZone.setText("-"+temp.toString());
                                    }
                                }
                            }
                        }
                    });


                        OperationArray[0].addActionListener(new ActionListener(){
                            public void actionPerformed(ActionEvent e){
                                if(e.getSource()==OperationArray[0]){
                                    String temp = WritingZone.getText();
                                    String temp2 = "";
                                    WritingZone.setText("");
                                    for (int x = 0 ; x < temp.length()-1 ; x++){
                                        temp2+=(Character.toString(temp.charAt(x)));
                                    }
                                    WritingZone.setText(temp2);
                                }
                            }
                        });

                        OperationArray[1].addActionListener(new ActionListener(){
                            public void actionPerformed(ActionEvent e){
                                if (e.getSource()==OperationArray[1]){
                                    WritingZone.setText("");
                                    first = 0;
                                    second = 0;
                                }
                            }
                        });

                        OperationArray[2].addActionListener(new ActionListener(){
                            public void actionPerformed(ActionEvent e){
                                first = Double.valueOf(WritingZone.getText());
                                WritingZone.setText("");
                                operation=OperationArray[2].getText().charAt(0);
                            }
                        });

                        OperationArray[3].addActionListener(new ActionListener(){
                            public void actionPerformed(ActionEvent e){
                                first = Double.valueOf(WritingZone.getText());
                                WritingZone.setText("");
                                operation=OperationArray[3].getText().charAt(0);
                            }
                        });

                        OperationArray[4].addActionListener(new ActionListener(){
                            public void actionPerformed(ActionEvent e){
                                first = Double.valueOf(WritingZone.getText());
                                WritingZone.setText("");
                                operation=OperationArray[4].getText().charAt(0);
                            }
                        });

                        OperationArray[5].addActionListener(new ActionListener(){
                            public void actionPerformed(ActionEvent e){
                                first = Double.valueOf(WritingZone.getText());
                                WritingZone.setText("");
                                operation=OperationArray[5].getText().charAt(0);
                            }
                        });

                        OperationArray[6].addActionListener(new ActionListener(){
                            public void actionPerformed(ActionEvent e){
                                String temp = String.valueOf(result);
                                String temp2 = WritingZone.getText();
                                WritingZone.setText("");
                                WritingZone.setText(temp2+""+temp);
                            }
                        });


                        OperationArray[7].addActionListener(new ActionListener(){
                            public void actionPerformed(ActionEvent e){
                                if (operation=='*'){
                                    String temp = WritingZone.getText();
                                    WritingZone.setText("");
                                    second = Double.valueOf(temp);
                                    result=(first*second);
                                    String temp2 = String.valueOf(result);
                                    WritingZone.setText(temp2);
                                }
                                else if(operation=='/'){
                                    String temp = WritingZone.getText();
                                    WritingZone.setText("");
                                    second = Double.valueOf(temp);
                                    if(second<0){
                                        result=(first/second);
                                        String temp2 = String.valueOf(result);
                                        WritingZone.setText(temp2);

                                    }
                                    else if (second>0){
                                        result=(first/second);
                                        String temp2 = String.valueOf(result);
                                        WritingZone.setText(temp2);

                                    }
                                    else if (second==0)
                                        WritingZone.setText("Error! Can't divide by 0");
                                }
                                else if (operation=='+'){
                                    String temp = WritingZone.getText();
                                    WritingZone.setText("");
                                    second = Double.valueOf(temp);
                                    result=(first+second);
                                    String temp2 = String.valueOf(result);
                                    WritingZone.setText(temp2);
                                }
                                else if (operation=='-'){
                                    String temp = WritingZone.getText();
                                    WritingZone.setText("");
                                    second = Double.valueOf(temp);
                                    result=(first-second);
                                    String temp2 = String.valueOf(result);
                                    WritingZone.setText(temp2);
                                }
                            }
                        });




                    final JPanel AllPanel = new JPanel();
                    AllPanel.setLayout(new BorderLayout(5,5));
                    AllPanel.add(BorderLayout.NORTH, TextPanel);
                    AllPanel.add(BorderLayout.CENTER, Finalpanel);
                    AllPanel.setBorder(BorderFactory.createTitledBorder("Simple      Calculator"));
                    emptyPanel.removeAll();
                    emptyPanel.add(AllPanel);
                    emptyPanel.setVisible(true);
                    pack();


            }}
        }



        });

        b2.addActionListener(new ActionListener(){
            public void actionPerformed(ActionEvent e){
                if(e.getSource()==b2)
                    System.exit(0);
            }
        });}
    @Override
    public void actionPerformed(ActionEvent e) {
        // TODO Auto-generated method stub

    }
    public static void main (String [] arg){






    JFrame frame = new Calculator ();
    frame.setVisible(true);
    frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    frame.setLocationRelativeTo(null);
    frame.pack();
    frame.setResizable(false);}}

Just remove all components from emptyPanel, NumberPanel,OperationPanel

emptyPanel.removeAll();
NumberPanel.removeAll();
OperationPanel.removeAll();