I have very similar problems. I posted the following as a helpdesk ticket, and the response was they weren't able to help and they referred me here. Here is what I said to the Helpdesk:
Problem 1, This happens in both version 3.10 and 3.63.
If the game window is centered, or on the right half, of my desktop, the cursor disappears when I move it over the contents of the game window. It will reappear on the other side of the window if I keep moving the mouse. Also, it does work over the blue bar at the top of the window, so I can move the window around on the desktop.
If I move the window to the far left of the desktop so the left edges of each are flush with each other, the cursor works within the window, Could this be related to the fact that the desktop is a widescreen (16:9) fomat?
In version 3.10, the box at the top of the window to either maximize or resize the window is grayed out and not working. (The minimize and close window functions work).
In version 3.63, the box at the top of the window to either maximize or resize the window works to a degree, but maximizing it only fills about 1/3 of the available screen. I cannot enlarge the window to take up any more of the desktop.