JButtons won't update on button click

Question 1

Building on to what this answer points out (using layout managers instead of setting size, as you should be doing) you could reset the the images just by looping through the components (JLabels) of the JPanel and changing their icons.

This particular example uses JLabels with MouseListeners but it could easily be switched to JButtons with ActionListeners

newGame.addActionListener(new ActionListener(){
    public void actionPerformed(ActionEvent e) {
         reset(iconPanel, icons);               <--- call reset method from below
         score = 0;
         scoreField.setText(String.valueOf(score));
    }
});
....

private void reset(JPanel panel, ImageIcon[] icons) {
    Component[] comps = panel.getComponents();
    Random random = new Random();
    for(Component c : comps) {
        if (c instanceof JLabel) {
            JLabel button = (JLabel)c;
            int index = random.nextInt(icons.length);
            button.setIcon(icons[index]);
        }
    }
}

enter image description here

Here's the complete running code. You just need to replace the image paths.

import java.awt.BorderLayout;
import java.awt.Color;
import java.awt.Component;
import java.awt.FlowLayout;
import java.awt.GridLayout;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.awt.event.MouseAdapter;
import java.awt.event.MouseEvent;
import java.util.Random;
import javax.swing.ImageIcon;
import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JLabel;
import javax.swing.JPanel;
import javax.swing.JTextField;
import javax.swing.SwingUtilities;
import javax.swing.border.LineBorder;

public class CircleImages {

    private int score = 0;
    private JTextField scoreField = new JTextField(10);

    public CircleImages() {
        scoreField.setEditable(false);

        final ImageIcon[] icons = createImageIcons();
        final JPanel iconPanel = createPanel(icons, 8);

        JPanel bottomLeftPanel = new JPanel(new FlowLayout(FlowLayout.LEADING));
        bottomLeftPanel.add(new JLabel("Score: "));
        bottomLeftPanel.add(scoreField);

        JPanel bottomRightPanel = new JPanel(new FlowLayout(FlowLayout.TRAILING));
        JButton newGame = new JButton("New Game");
        bottomRightPanel.add(newGame);
        JButton quit = new JButton("Quit");
        bottomRightPanel.add(quit);

        JPanel bottomPanel = new JPanel(new GridLayout(1, 2));
        bottomPanel.add(bottomLeftPanel);
        bottomPanel.add(bottomRightPanel);

        newGame.addActionListener(new ActionListener(){
            public void actionPerformed(ActionEvent e) {
                reset(iconPanel, icons);
                score = 0;
                scoreField.setText(String.valueOf(score));
            }
        });

        JFrame frame = new JFrame();
        frame.add(iconPanel);
        frame.add(bottomPanel, BorderLayout.PAGE_END);
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        frame.pack();
        frame.setLocationRelativeTo(null);
        frame.setVisible(true);
    }

    private void reset(JPanel panel, ImageIcon[] icons) {
        Component[] comps = panel.getComponents();
        Random random = new Random();
        for(Component c : comps) {
            if (c instanceof JLabel) {
                JLabel button = (JLabel)c;
                int index = random.nextInt(icons.length);
                button.setIcon(icons[index]);
            }
        }
    }

    private JPanel createPanel(ImageIcon[] icons, int gridSize) {
        Random random = new Random();
        JPanel panel = new JPanel(new GridLayout(gridSize, gridSize));
        for (int i = 0; i < gridSize * gridSize; i++) {
            int index = random.nextInt(icons.length);
            JLabel label = new JLabel(icons[index]);
            label.addMouseListener(new MouseAdapter(){
                public void mouseClicked(MouseEvent e) {
                    score += 1;
                    scoreField.setText(String.valueOf(score));
                }
            });
            label.setBorder(new LineBorder(Color.GRAY, 2));
            panel.add(label);
        }
        return panel;
    }

    private ImageIcon[] createImageIcons() {
        String[] files = {"blackcircle.png",
            "bluecircle.png",
            "greencircle.png",
            "greycircle.png",
            "orangecircle.png",
            "redcircle.png",
            "yellowcircle.png"
        };
        ImageIcon[] icons = new ImageIcon[files.length];
        for (int i = 0; i < files.length; i++) {
            icons[i] = new ImageIcon(getClass().getResource("/circles/" + files[i]));
        }
        return icons;
    }

    public static void main(String[] args) {
        SwingUtilities.invokeLater(new Runnable() {
            public void run() {
                new CircleImages();
            }
        });
    }
}

Question 2

You are creating a new set of buttons in resetButtons2() and placing them on top (or rather under) of the already existing set of buttons in the same locations. You should create the set of buttons once and only update their icons upon reset.

You should do a number of things:

Use a proper layout manager, e.g., GridLayout
Create the 8x8 grid of buttons only once and replace their icons when needed
Call invalidate/repaint to refresh the content pane

And for a JFrame you don't need getContentPane().add(...), you can directly do add(...)

Question 3

Two things.

First, make sure you remove the existing buttons first. Alternatively, you could simply update the state of the buttons. This would require you to create an array or List of buttons first, which your reset method would then iterate over and update their properties as required.

Second, make use of an appropriate layout manager. A null layout ias a very bad idea. You do not control the font metrics of the underlying platform and this will change how your buttons look on different systems, making your UI less dynamic then it should be