I tested three issues:
White screen until resized issues: I can confirm that with desktop composition enable on my system the white screen behavior doesn't happen when MC is opened on the first desktop, but does happen on the second desktop when MC is opened there after a desktop change (as you described). The behavior also goes away when JRiver is moved to the first desktop. But that is only true if I have desktop composition enabled; when composition is disabled (which it is by default on my system), I still get white screen behavior even when opening on the first screen.
Moving: I have no issues moving any JRiver windows on any desktop screen.
Resizing:
1) Main window:
Mouse initiated resizing: Resizing the main MC window using the mouse doesn't usually work; I seem to have trouble getting the cursor to acknowledge that I'm at a boundary to engage resizing. It doesn't matter if I try the bottom right corner or any other corner or edge. It's basically one out of ten times that I get the necessary cursor change when at a boundary, which is not the behavior I see with any other windows (including JRiver child windows, like the one generated by tools>options). These effects are independent of which numbered desktop I'm on.
Window manager initiated resizing: If I try to use the "resize" command from the window manager it works fine provided my mouse is already in the lower right hand corner and I execute the resize with a hotkey, but although it works, it seems to cause CPU spikes and strobing. These effects are independent of which numbered desktop I'm on.
Title bar buttons: The JRiver main window minimize/iconify window button works correctly, but the maximize window button does not work at all (no response when pressed). Using the window manager to maximize the main window (i.e. hotkeys or right clicking on the application in the application panel and maximizing that way) works correctly most of the time.
2) Child windows: All JRiver child windows work normally for resizing purposes (have a title bar, all buttons work, edge resizing works fine).
[Testing environment is XFCE using openbox as window manager on Arch Linux; using Compton as my standalone compositor]