Con el JDateChooser resuelves tu primera cuestión:

http://max-server.myftp.org/jcalendar/ibuild/dist/doc/api/

Este componente tiene los listeners necesarios.

Sobre la segunda cuestión, aquí tienes información muy abundante:

http://docs.oracle.com/javase/tutorial/uiswing/components/formattedtextfield.html
http://docs.oracle.com/javase/7/docs/api/javax/swing/JFormattedTextField.html
http://www.java2s.com/Code/Java/Swing-JFC/Formatted-TextField.htm

Un test de ejemplo, por si te sirve de guía.

import com.toedter.calendar.JDateChooser;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import java.beans.PropertyChangeEvent;
import java.beans.PropertyChangeListener;
import java.sql.Date;
import java.text.ParseException;
import java.util.Objects;
import java.util.logging.Level;
import java.util.logging.Logger;
import javax.swing.text.MaskFormatter;

public class NewJFrame extends javax.swing.JFrame {

private MaskFormatter mask;

public NewJFrame() {

try {
mask = new MaskFormatter("####-##-##");
} catch (ParseException ex) {
Logger.getLogger(NewJFrame.class.getName()).log(Level.SEVERE, null, ex);
}
mask.setPlaceholderCharacter('_');

initComponents();

jFormattedTextFieldFecha.addActionListener(new ActionListener() {

@Override
public void actionPerformed(ActionEvent e) {
String fecha = jFormattedTextFieldFecha.getText();
Date fechaSQL = Date.valueOf(fecha);
System.out.println("fecha SQL: " + fechaSQL);
}
});

jPanelDateChooser.addPropertyChangeListener(new PropertyChangeListener() {

@Override
public void propertyChange(PropertyChangeEvent evt) {
if ("date".equals(evt.getPropertyName())) {
jTextFieldFechaSeleccionada.setText(Objects.toString(evt.getNewValue()));

}
}
});
}

/** This method is called from within the constructor to
initialize the form.
WARNING: Do NOT modify this code. The content of this method is
always regenerated by the Form Editor.
*/
@SuppressWarnings("unchecked")
// <editor-fold defaultstate="collapsed" desc="Generated Code">
private void initComponents() {

jPanelDateChooser = new JDateChooser();
jTextFieldFechaSeleccionada = new javax.swing.JTextField();
jFormattedTextFieldFecha = new javax.swing.JFormattedTextField(mask);

setDefaultCloseOperation(javax.swing.WindowConstants.EXIT_ON_CLOSE);

javax.swing.GroupLayout layout = new javax.swing.GroupLayout(getContentPane());
getContentPane().setLayout(layout);
layout.setHorizontalGroup(
layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
.addGroup(layout.createSequentialGroup()
.addContainerGap()
.addComponent(jPanelDateChooser, javax.swing.GroupLayout.PREFERRED_SIZE, 125, javax.swing.GroupLayout.PREFERRED_SIZE)
.addPreferredGap(javax.swing.LayoutStyle.ComponentPlacement.UNRELATED)
.addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
.addComponent(jFormattedTextFieldFecha, javax.swing.GroupLayout.DEFAULT_SIZE, 245, Short.MAX_VALUE)
.addComponent(jTextFieldFechaSeleccionada))
.addContainerGap())
);
layout.setVerticalGroup(
layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
.addGroup(layout.createSequentialGroup()
.addContainerGap()
.addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.TRAILING)
.addComponent(jPanelDateChooser, javax.swing.GroupLayout.PREFERRED_SIZE, 24, javax.swing.GroupLayout.PREFERRED_SIZE)
.addComponent(jTextFieldFechaSeleccionada, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE))
.addPreferredGap(javax.swing.LayoutStyle.ComponentPlacement.UNRELATED)
.addComponent(jFormattedTextFieldFecha, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE)
.addContainerGap(javax.swing.GroupLayout.DEFAULT_SIZE, Short.MAX_VALUE))
);

layout.linkSize(javax.swing.SwingConstants.VERTICAL, new java.awt.Component[] {jFormattedTextFieldFecha, jPanelDateChooser, jTextFieldFechaSeleccionada});

pack();
}// </editor-fold>

/**
@param args the command line arguments
*/
public static void main(String args[]) {
/* Create and display the form */
java.awt.EventQueue.invokeLater(new Runnable() {
@Override
public void run() {
new NewJFrame().setVisible(true);
}
});
}
// Variables declaration - do not modify
private javax.swing.JFormattedTextField jFormattedTextFieldFecha;
private javax.swing.JPanel jPanelDateChooser;
private javax.swing.JTextField jTextFieldFechaSeleccionada;
// End of variables declaration
}