I added two JMenu's on the frame :

JFrame frame = new JFrame();
//Menu :
menuBar = new JMenuBar();
menu = new JMenu("Fichier");
menu2 = new JMenu("Options");
JSeparator sep = new JSeparator(SwingConstants.VERTICAL);
JButton btn = new JButton();
btn.addActionListener(MyListener);
menuBar.add(menu);
menuBar.add(sep);
menuBar.add(menu2);
frame.setJMenuBar(menuBar);

The result I want :

import java.awt.EventQueue;
import javax.swing.JFrame;
import javax.swing.JScrollPane;
import javax.swing.JTextArea;

public class Test {

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

    public Test() {
        EventQueue.invokeLater(new Runnable() {
            @Override
            public void run() {                
                JTextArea ta = new JTextArea(20, 40);

                JFrame frame = new JFrame();
                frame.setUndecorated(true);
                frame.add(new JScrollPane(ta));
                frame.pack();
                frame.setLocationRelativeTo(null);
                frame.setVisible(true);
            }
        });
    }
}

Now, if you "need" some padding around the edges, either use a layout manager that allows you to specify padding or use a EmptyBorder

import java.awt.BorderLayout;
import java.awt.EventQueue;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.JScrollPane;
import javax.swing.JTextArea;
import javax.swing.border.EmptyBorder;

public class Test {

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

    public Test() {
        EventQueue.invokeLater(new Runnable() {
            @Override
            public void run() {
                JTextArea ta = new JTextArea(20, 40);

                JFrame frame = new JFrame();
                JPanel content = new JPanel(new BorderLayout());
                content.setBorder(new EmptyBorder(16, 16, 16, 16));
                frame.setContentPane(content);
                frame.setUndecorated(true);
                frame.add(new JScrollPane(ta));
                frame.pack();
                frame.setLocationRelativeTo(null);
                frame.setVisible(true);
            }
        });
    }
}

I think you will find:

• Creating a GUI With Swing
• How to Make Frames (Main Windows)
• Laying Out Components Within a Container

a better place to start.

Also, in future, ask 1 specific question, otherwise you risk having the question closed for "needing more focus"