Sessions & ContentPlaceHolders

Question 1

Firstly, you have a ContentPlaceHolder inside another ContentPlaceHolder and I can't see any reason for this.

<asp:ContentPlaceHolder ID="ContentPlaceHolder3" runat="server">
   <asp:ContentPlaceHolder id="ContentPlaceHolder2" runat="server">

To the matter in hand, I would hide the controls contained within the ContentPlaceHolder depending on whether the user is logged in or not, rather than hiding the placeholder, however this is up to you. I would also add the userid column to your SQL query.

The follwing should get you started, note this is untested off the top of my head:

SELECT userid, username, password FROM users ....

If dr.HasRows Then
  Session("userid") = dr("userid")
ElseIf dr.HasRows = False Then
   lblRegister.ForeColor = Drawing.Color.Red
   lblRegister.Text = "Incorrect Username/Password."
End If

Now that you have this, you can check the Session variable on Page_Load to see if the user is logged in.

Protected Sub Page_Load(sender As Object, e As EventArgs)
  If Session("userid") <> "" Then
    txtLoginUser.Visible = False
    txtLoginPass.Visible = False
  Else
    'Set your label text here, query the database to get the First and Second name of the user using the `userid`
  End If
End Sub

EDIT You need to close your readers after you have finished reading:

dr.Close() and datareader.Close()

Also this line lblLoggedIn.Text = "Welcome," + txtLoginUser.Text needs to be:

lblLoggedIn.Text = datareader("name").ToString() & " " &
datareader("surname").ToString()

Question 2

Ideally, you want to use ASP.Net LoginView and LoginStatus control.

Since you only have one page, just use two Panels - show and hide based on user is Authenticated or not.

NOTE: do not use ContentPlaceHolder for this case.

Update:

Here is the sample code for LoginView if you want to try. It is a prefer way of doing it.

%@ Page Language="C#" AutoEventWireup="true" CodeBehind="WebForm6.aspx.cs" 
    Inherits="WebApplication2010.WebForm6" %>

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" 
    "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title></title>
</head>
<body>
    <form id="form1" runat="server">
    <asp:LoginView ID="LoginView1" runat="server">
        <AnonymousTemplate>
            <asp:Label ID="lblUsername" runat="server" Font-Bold="True" Text="U:"></asp:Label>
            &nbsp;<asp:TextBox ID="txtLoginUser" runat="server" BorderStyle="None" BorderWidth="0px"
                TextMode="Password" Wrap="False"></asp:TextBox>
            &nbsp;
            <asp:Label ID="lblUsername0" runat="server" Font-Bold="True" Text="P:"></asp:Label>
            <asp:TextBox ID="txtLoginPass" runat="server" BorderStyle="None" BorderWidth="0px"
                TextMode="Password" Wrap="False"></asp:TextBox>
            &nbsp;
            <asp:Button ID="btnLogin" runat="server" BorderStyle="None" OnClick="Button1_Click"
                Text="Login" />
        </AnonymousTemplate>
        <LoggedInTemplate>
            Welcome!
        </LoggedInTemplate>
    </asp:LoginView>
    </form>
</body>
</html>

protected void Button1_Click(object sender, EventArgs e)
{
    var txtLoginUser = LoginView1.FindControl("txtLoginUser") as TextBox;
    var txtLoginPass = LoginView1.FindControl("txtLoginPass") as TextBox;

    // Your authentication

    // If validation is successful, create Authentication ticket
    FormsAuthentication.SetAuthCookie(txtLoginUser.Text, false);
}