That's a pretty awesome case / stand there!!
As for the 3 axis 9 button thing, while it's perhaps strange that FSX doesn't recognize it by name, that is indeed the proper amount of axis and buttons that the Saitek quadrant has. The three bottom rocker switches are two buttons each (up & down), and the bottom / reverse range of each throttle axis is a button.
Wish I could help on the trim wheel, but I've had mine long enough that I don't recall ever having to do anything special to get it to work.