Could someone point me in the right direction, for Tray Notification Windows, similar to the example below:

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There’s a simple interface to the notification tray called NotifyIcon in WinForms.
Once you can grab its events (Clicked, DoubleClicked, etc.) you can pick whether you want to show a context-menu or a form.
As noted by schlingel, in the example you provided is a custom form without a window border, drawn right next to the notification tray.