One day I tried to play around with printscreening closed windows. (You really cant since its not being draw)
Found a way, making it invisible, opening it open, taking the screenshot, minimize it and make it visible again. (in a few ms)
Cant help you exactly with the rest tho, not sure how that could work, never really tried tbh. :\ But I guess WinAPI should have something more to help you with that, which I might have missed, usually happens.