Lots of interesting questions.
If you have full workshop facilities you will have no trouble lining things up but most constructors have to do the best they can with what they have.
If your stator mounts don't line up it is easy to use washers to shim things to the correct position. Hold the stator temporarily in place and see what gaps you need to shim. I wouldn't leave nuts loose, it's better to get the things lined up with washers or thin bits of shim so that you can tighten the nuts properly. If you loctite the nuts they will hold ok but you may get fretting from the inevitable vibration if things are too loose. I wouldn't worry too much on the one you done, but try to get the next one lined up and tight.
When you widen the gap it doesn't matter if the stator is not in the centre as long as it clears the magnets, the air gap is the distance between magnets and the flux there is fairly linear and consistent so having equal clearances is not essential.
With 23v at 60 rpm you will have a low battery cut in about 120 rpm. That is rather slow for a 8ft prop, it may give you good very low wind performance but I think it will kill your output in the most productive wind speed.
You could increase prop size if you are in a low wind area to advantage, up to about 9ft should be safe for the rest of the structure and hub. The main concern is that you can control the thing in high winds without burning the stator. Any increase in prop diameter ought to be accompanied by an increase in alternator offset to keep the furling safe. As you will be running further from stall it will be more lively and more difficult to control so make sure the tail is light to start with and increase weight if it furls too early. If you get regular high winds in your area I would not increase the prop size but increase the air gap and possibly add line resistance to get it out of stall to make it perform properly.
Flux