form.close() is not working

Well, per what you are showing here, you are never really displaying the Form1 instance that you are creating, that is, you are creating a Form1 called 'f' and then you are closing it.  Your application is tied to the existence of the original form 1 (look at the main function is the Program.cs file and you will see this).  If anything happens to the original Form1, it and any other forms you may have opened will all close together as form1 dies.

To be able to close Form1, you will need to rewrite the Program.cs file's main function to do something like this (I commented out the default line that will be added by the IDE).  In this format, the application is not dependent upon the continued existence of Form1.

static void Main()
{
     Application.EnableVisualStyles();
     Application.SetCompatibleTextRenderingDefault(false);
     //Application.Run(new Form1());
     Form1 f = new Form1();
     f.Show();
     Application.Run();
}

As for the use of visibility as a property used to show the form, replace that with 'Show' as indicated above.  Your button click event handler ought to look something like this (and also use 'Dispose' instead of 'Close'):

private void btnExit_Click(object sender, EventArgs e)
{
     Form1 f = new Form1();
     f.Text = "Form 2";
     f.Show();
     this.Dispose();
}

Now, you have one last problem.  If you close Form2, the application is still running and you won't have a nice way to exit the application.  You will need to give yourself another button to exit the application instead of closing Form1 or Form2, the click event handler for this other button should call 'Application.Exit()'.  If you intend to exit the application whenever Form2 is closed, you may want to consider adding an event handler for the Form2_FormClosed event and in the handler, call Application.Exit.

Having said this much, this is not a very sound way to handle an application because, you cannot account for the disposal for Form1 by calling for the application to exit; therefore, if the user did not click the button and create an instance of Form2, and they closed Form1, the application would still be running even though it no longer supplies an interface to the user and there is no longer a way to exit the application.