You can use keyboard to close or open any task or window program. You need to use Tab button very frequently to do this task.
If mouse cursor hangs during working, only way is to unplug the USB mouse (I have experienced this type of cursor hangs and that to with USB mouse only). and plug it again.
Last option is to give some time say, 5 minutes which allows the inside process to stop and your curor might appear and moves. If this does not work, press Ctrl+Alt+Del to open task manager and close the program by Keyboard Tab keys.