Inserted Row Selection jTable

Question 1

There are several things wrong...

Avoid KeyListener, there are a swagger of problems associated with using KeyListeners which the key bindings API fixes
You select the row by using table.setRowSelectionInterval(rowCount-1,rowCount-1);, but rowCount is no longer valid, as you've added a new row
transferFocus is used to transfer focus to the next focusable component, which will mean that the JTable would mostly likely lose focus, pretty sure this isn't what you want.

For example...

import java.awt.EventQueue;
import java.awt.event.ActionEvent;
import java.awt.event.KeyEvent;
import java.util.Vector;
import javax.swing.AbstractAction;
import javax.swing.ActionMap;
import javax.swing.InputMap;
import javax.swing.JFrame;
import javax.swing.JScrollPane;
import javax.swing.JTable;
import javax.swing.KeyStroke;
import javax.swing.UIManager;
import javax.swing.UnsupportedLookAndFeelException;
import javax.swing.table.DefaultTableModel;

public class TestTable {

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

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

                DefaultTableModel model = new DefaultTableModel(4, 4);
                JTable table = new JTable(model);

                InputMap im = table.getInputMap();
                im.put(KeyStroke.getKeyStroke(KeyEvent.VK_TAB, 0), "CellAction");

                ActionMap am = table.getActionMap();
                am.put("CellAction", new CellAction(table));

                JFrame frame = new JFrame("Testing");
                frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
                frame.add(new JScrollPane(table));
                frame.pack();
                frame.setLocationRelativeTo(null);
                frame.setVisible(true);
            }
        });
    }

    public class CellAction extends AbstractAction {

        private JTable table;

        public CellAction(JTable table) {
            this.table = table;
        }

        @Override
        public void actionPerformed(ActionEvent e) {
            int column = table.getSelectedColumn();
            int rowCount = table.getRowCount();
            int currentRow = table.getSelectedRow();
            if (currentRow == rowCount - 1) {
                table.editCellAt(currentRow, column);
            }
            if (column == 3 && currentRow == rowCount - 1) {
                DefaultTableModel model = (DefaultTableModel) table.getModel();
                Vector row = new Vector();
                row.add(null);
                row.add(null);
                row.add(null);
                row.add(null);

                model.addRow(row);
            }
            if (column == 3) {
                currentRow++;
                column = 0;
                table.setRowSelectionInterval(currentRow, currentRow);
                table.setColumnSelectionInterval(column, column);
                table.editCellAt(currentRow, column);
            }
        }

    }

}

Question 2

Seems problem in misspelling, just change

table.setRowSelectionInterval(rowCount-1,rowCount-1); to

jTable1.setRowSelectionInterval(rowCount-1,rowCount-1);.

Because table is null. And everywhere you use jTable1.