The 'wool bar' is a distaff. It is not needed.
These are plans for a single drive wheel, except it does not have the brake band for the bobbin whorl (actually a pulley). It would behoove you to make the diameter of the bobbin whorl different than the flyer whorl for either a single drive (SD) or a double drive (DD). If your flyer whorl has 2 diameters, you'll even be better off.
Castle (upright) wheels as just as functional as saxony wheels. Take a look at the Ashford Traveller
wheels (both SD & DD)
The 'wool carrier' is just a piece for the distaff. Neither is needed.
The table may or may not have a place to keep extra bobbins. The lazy kate is a separate piece all together. I generally keep my extra bobbins on my kate and not on my wheel, since it is easier to ply from my kate when it is behind my working hand.