List all the files inside a speciifc directory / folder

Well, if the TextBox is already on Form1 and you want it to display the selected file in the ListView, if there is one, whenever the selection changes, then you need to add a handler for the ListView's SelectedIndexChanged event.

This could be done by adding the handler (manually) to Form1 or, more conveniently, by using a  lambda expression within the calling code:

            listView1.View = View.List;
            listView1.Location = new System.Drawing.Point(0, 0);
            listView1.Name = "listView1";
            listView1.Size = new System.Drawing.Size(200, 150);

            Form1 form1 = new Form1();
            form1.Controls.Add(listView1);
            listView1.SelectedIndexChanged += (object sender, EventArgs e)
 =>
 {
     if (listView1.SelectedIndices.Count > 0)
     {
         form1.textBox1.Text = listView1.SelectedItems[0].Text;
     }
     else
     {
         form1.textBox1.Text = "";
     }
 };
           form1.Show();

I note that you've changed the TextBox's Modifiers property to public and so you should be able to access it directly (as I've done above) without going through the Controls collection.