As stated, there is an arrow on the trackball that shows which direction to orient it. Also as stated, if you have to mount it in a different orientation, you can swap the axes pins (the actual pins in the plug, not the plugs) to get it right. The pins in question are the center pins, not the outside pins, leave those alone and still plug them in to the proper places on your encoder.
The top buttons will be a little bit of a challenge when building the housing for the CP, but otherwise you have enough clearance. The only admin buttons I would do would be a select button, a pause, an exit, and maybe a mute. Don't put them in the path of your trackball or you will inevitably hit the exit when playing golden tee or shuffleshot..
any time you put a control above another, you will want to set the control panel to the height and angle it will rest when complete, and then stand in front of it and use each control as if you are playing a game. You will find that some controls are awkward to handle, leave you in uncomfortable positions, or are just plain in the way of other controls. Since you already cut your panel out, set it up and get your hands on it and see. Don't be afraid to start over at this point, you don't have art on it yet, so it can always be redone.
They don't make a hole saw that is a perfect fit for that trackball, and IMHO a holesaw makes a pretty ragged cut even when you are careful, so my advice would be to make a test piece, cut the hole the way you plan to, and see if you like the fit. I wrote a little tutorial in the woodworking section on using a router and the trim ring to cut a perfect hole for the ultimarc trackball, might want to peek at it even if you are just going to use a hole saw that is a few mm too big.