Java GridBagLayout resizing and fixed size

Question 1

You need to supply weightx and weighty values with the GridBagConstraints which affect how the individual components react to changes in the size the parent container and how much "weight" the take up within the given cell

Take a look at How to use GridBagLayout for more details

import java.awt.BorderLayout;
import java.awt.Color;
import java.awt.Dimension;
import java.awt.EventQueue;
import java.awt.GridBagConstraints;
import java.awt.GridBagLayout;
import java.awt.GridLayout;
import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.UIManager;
import javax.swing.UnsupportedLookAndFeelException;

public class TestGridBagLayout {

    public static void main(String[] args) {
        new TestGridBagLayout();
    }

    private JPanel mainPanel;
    private JPanel p1;
    private JPanel p2;
    private JPanel p3;

    public TestGridBagLayout() {
        EventQueue.invokeLater(new Runnable() {
            @Override
            public void run() {
                try {
                    UIManager.setLookAndFeel(UIManager.getSystemLookAndFeelClassName());
                } catch (ClassNotFoundException | InstantiationException | IllegalAccessException | UnsupportedLookAndFeelException ex) {
                }

                mainPanel = new JPanel();
                mainPanel.setLayout(new GridBagLayout());
                GridBagConstraints c = new GridBagConstraints();

                //P1    FILL P1 WITH 64 BUTTONS
                p1 = new JPanel();
                p1.setLayout(new GridLayout(8, 8));

                p1.setMinimumSize(new Dimension(600, 600));
                p1.setMaximumSize(new Dimension(600, 600));
                p1.setPreferredSize(new Dimension(600, 600));

                for (int y = 0; y < 8; y++) {
                    for (int x = 0; x < 8; x++) {
                        JButton btn = new JButton(x + " , " + y);
                        p1.add(btn);
                    }
                }

                //P2    FILL P2 WITH 4 BUTTONS
                p2 = new JPanel();
                p2.setLayout(new GridLayout(4, 1));
                p2.setMinimumSize(new Dimension(150, 100));
                p2.setMaximumSize(new Dimension(150, 100));
                p2.setPreferredSize(new Dimension(150, 100));

                for (int i = 0; i < 4; i++) {
                    p2.add(new JButton("Button"));
                }

                //P3
                p3 = new JPanel();
                p3.setMinimumSize(new Dimension(100, 150));
                p3.setMaximumSize(new Dimension(100, 150));
                p3.setPreferredSize(new Dimension(100, 150));
                p3.setBackground(Color.BLUE);

                //ADD ALL TO mainPanel
                c.gridx = 0;
                c.gridy = 0;
                c.fill = GridBagConstraints.BOTH;
                c.weightx = 1;
                c.weighty = 1;
                mainPanel.add(p1, c);

                c.gridx = 1;
                c.gridheight = 2;
                c.weighty = 1;
                c.weightx = 0;
                c.fill = GridBagConstraints.VERTICAL;
                mainPanel.add(p2, c);

                c.gridx = 0;
                c.gridy = 1;
                c.gridheight = 1;
                c.gridwidth = 2;
                c.fill = GridBagConstraints.HORIZONTAL;
                c.weighty = 0;
                c.weightx = 1;
                mainPanel.add(p3, c);

                JFrame frame = new JFrame("Testing");
                frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
                frame.setLayout(new BorderLayout());
                frame.add(mainPanel);
                frame.pack();
                frame.setLocationRelativeTo(null);
                frame.setVisible(true);
            }
        });
    }

}

Question 2

I would consider using nested JPanels that use BorderLayouts instead. For instance:

import java.awt.BorderLayout;
import java.awt.Color;
import java.awt.Dimension;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;

import javax.swing.*;

public class EmielGui extends JPanel {
   protected static final int DELTA_DIMEN = 1;
   protected static final int MAX_DIMEN = 600;
   private static final int DELAY = 20;
   private JPanel rightPanel = new JPanel();
   private JPanel bottomPanel = new JPanel();
   private JPanel centerPanel = new JPanel();
   private int dimen = 100;

   public EmielGui() {
      JPanel tempCenterPanel = new JPanel(new BorderLayout());
      tempCenterPanel.add(centerPanel, BorderLayout.CENTER);
      tempCenterPanel.add(bottomPanel, BorderLayout.SOUTH);

      setLayout(new BorderLayout());
      add(rightPanel, BorderLayout.EAST);
      add(tempCenterPanel, BorderLayout.CENTER);

      rightPanel.setMinimumSize(new Dimension(150, 0));
      bottomPanel.setMinimumSize(new Dimension(0, 150));

      rightPanel.setPreferredSize(rightPanel.getMinimumSize());
      bottomPanel.setPreferredSize(bottomPanel.getMinimumSize());

      rightPanel.setBorder(BorderFactory.createLineBorder(Color.red));
      bottomPanel.setBorder(BorderFactory.createLineBorder(Color.blue));
      centerPanel.setBorder(BorderFactory.createLineBorder(Color.green));

      new Timer(DELAY, new ActionListener() {

         @Override
         public void actionPerformed(ActionEvent e) {
            dimen += DELTA_DIMEN;
            if (dimen < MAX_DIMEN) {
               centerPanel.setPreferredSize(new Dimension(dimen, dimen));
               SwingUtilities.getWindowAncestor(EmielGui.this).pack();

            } else {
               ((Timer) e.getSource()).stop();
            }
         }
      }).start();
   }

   private static void createAndShowGui() {
      EmielGui mainPanel = new EmielGui();

      JFrame frame = new JFrame("EmielGui");
      frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
      frame.getContentPane().add(mainPanel);
      frame.pack();
      frame.setLocationByPlatform(true);
      frame.setVisible(true);
   }

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