Form position on lower right corner of the screen

Override the Form Onload and set the new location :

protected override void OnLoad(EventArgs e)
{
    var screen = Screen.FromPoint(this.Location);
    this.Location = new Point(screen.WorkingArea.Right - this.Width, screen.WorkingArea.Bottom - this.Height);
    base.OnLoad(e);
}

I don't currently have multiple displays to check, but it should be something like

    public partial class LowerRightForm : Form
    {
        public LowerRightForm()
        {
            InitializeComponent();
        }

        protected override void OnLoad(EventArgs e)
        {
            PlaceLowerRight();
            base.OnLoad(e);
        }

        private void PlaceLowerRight()
        {
            //Determine "rightmost" screen
            Screen rightmost = Screen.AllScreens[0];
            foreach (Screen screen in Screen.AllScreens)
            {
                if (screen.WorkingArea.Right > rightmost.WorkingArea.Right)
                    rightmost = screen;
            }

            this.Left = rightmost.WorkingArea.Right - this.Width;
            this.Top = rightmost.WorkingArea.Bottom - this.Height;
        }
    }