1. Not sure what the standard for piccolo basses are. Do a simple google search for your favorite piccolo bass model and see what its specs are.
2. Again, a google search for your favorite piccolo bass should yield some good results. At the very least, it should be able to give you some idea of the range of appropriate string gauges.
3. In order to calculate neck width, you need to know the string spacing. Again, because I don't know piccolo bass standard specs (if there is such a thing as standard specs for pic basses), a google search should yield some results. One thing you should be aware of is whether or not you will be able to use your current neck pocket, or whether you will need to route a bigger one. Your string spacing will be directly dependent on your neck pocket.
4. What do you plan on using for the nut material? If you are using wood (which I prefer -- elegant, and likely to give a more even tone, especially if it is the same wood as the fretboard). If so, just put an oversized blank in the nut slot. Once you get your bass built, set it up, and file the slots down to where they should be (can be lower than a normal bass, since there are no frets), then you can level off the top of the nut.
I'm not sure how much mwah you will be able to get with a piccolo bass. I mean... you are essentially playing a guitar (one of the reasons I never understood the concept of a piccolo bass to begin with). I'm not sure if the higher tuned/thinner gauged strings will yield much mwah, since the mwah effect is the result of the string itself, not the neck pickup. Besides, Jaco used his bridge pickup almost exclusively, and if that isn't enough mwah for ya, well, there's something wrong!
Hope that helped. Maybe some piccolo bass builders will chime in on the issue.