How I can I set a NotifyIcon to be always visible in the right tray: http://screensnapr.com/v/qKWHe2.png
because it shifts it over into the inactive icon window: http://
Giving notification area icons "always visible" status is a choice the user makes through the taskbar properties dialog. This is a design decision made by the appropriate Windows team in order to put this choice at the user's discretion.
For this reason, there is no programmatic interface that allows you to make an icon always visible. There's even no interface to ask if your icon is visible or not.
In your shoes I 'd just set up a hotkey that allows the user to take screenshots without getting involved with the icon at all (all screen capture programs do this).
If the user really likes to right click before taking a screenshot, they can always change their preference through taskbar properties as mentioned above.