No, you don't need new nuts. I can't say anything about pre-'05 Fits and I haven't looked at any online manual. But my printed manual doesn't say anything about how to align the car anyway. Basically my strategy was to install the bolts loosely, push in the strut as far as possible to obtain max negative camber, then tighten the bolts while I held the strut in that position. Then you have to get a wheel alignment done to get the camber as close as possible on each side and then set toe-in by adjusting the tie-rod ends. You'll be OK to drive the car a short distance to an alignment shop after installing the bolts, but I wouldn't take it on the freeway. You can also get the toe pretty close by eyeballing it and then drive it to a shop. You can also do the whole alignment yourself using the procedure I described here:
First look at stock camber...