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Creating a dynamic search box/table in Java

What I'm trying to achieve is a JTextField with a JTable on the bottom, every time a change occurs on the JTextField (type or delete a character) the JTable would update showing the results from it's list of strings that match what is written on the JTextField, and showing all results if empty.
What I don't know how to do :
How to set the event on the JTextField that triggers everytime its text changes
Making the JTable update its values in an efficient way, without using too much memory

Add a DocumentListener to your JTextField. Update the TableModel belonging to your JTable with matches. The JTable will update itself in response.

Which editing and removing row method is better for JTable?

I wanna ask that which method to edit a JTable is better than the other?
use setValueAt() function.
Make a new model of JTable and feed its object to JTable.
And also, how to remove a Row from JTable without using method 2 described above?

You would use the setValueAt method when you're changing one value at a time.
You would make a new TableModel when you're changing 25% or more of the rows at one time.
If you use a DefaultTableModel as your TableModel, you can use the addRow or setValueAt methods to add a row and change a row value. You can use the removeRow method to remove a row.
Since the TableModel is associated with the JTable, any changes to the TableModel are reflected in the JTable. Any changes to the JTable by the user are reflected in the TableModel.

Get the JScrollPane of a JTable

I have a JTable object. How can I get a reference to the JScrollPane the JTable is in?
I tried getParent() but that returns null.
EDIT:
My Bad.
As mentioned in one of the comments I'm trying to create my custom JTable that has a row header by default without manually having to add it. The problem is to add the row header one needs to call scrollPane.setRowHeaderView(rowHeader);. The problem is that I was calling getParent() in the constructor befpre the table actually has a parent and before jScrollPane1.setViewportView(jTable1); was called.
So this can't be solved in one step but only afterwards.

I think this is what you need:
JScrollPane scrollPane = (JScrollPane)SwingUtilities.getAncestorOfClass(JScrollPane.class, myTable);
You can find more information about this method here.

How to assign the auto complete text field to JTable cell?

I have created one Class for auto complete text fields.
I want to use that Class and try to include my JTable cell fields, but it won't display.
Please advice

you can to use AutoComplete JComboBox / JTextField
put this JComboBox / JTextField to the JTable as Renderer and Editor

(Assuming I understand the question)
You need to wrap your editor in TableCellEditor. Have a look at Using Other Editors an example.
Once you have it set up, you need to register the editor with the table.
One way is to register the editor with the column in question via the TableColumnModel
table.getColumnModel().getColumn(indexToColumnInQuestion).setCellEditor(tableCellAutoCompleteEditor);

Java AbstractTableModel repaint();

I have a problem in my table model to update the data I print in it.
I have the class AgendaTableModel who is the table model, and the class Screen that is the main UI, when I press the button 'Listar Contatos' the table model should appear on JScrollPane in the center of the JFrame, but it continues blank.
What should be the problem ?

You should really post the code or better an SSCCE.
Here's the Oracle's tutorial on JTable.
I'll give you some hints:
Each JTable has a TableModel associated
You don't display the TableModel but the JTable, that is a view of your model
When you add components dynamically you should revalidate the parent component, so if you are adding a JTable somewhere, try to revalidate its container.
If you are trying to add the JTable to an already existing JScrollPane (empty or containing something else), consider to instantiate a new JScrollPane rather than updating its content.