How to keep scratch art paper clean and free of pencil and eraser marks?
I have not done any sort of serious scratch-board art, but here are some suggestions, to answer your two part question:

Use black colored pencil instead of regular pencil.— it isn't as reflective as regular pencil, so you will just barely be able to see it while you're working.

Paint over the nicks/stray pencil marks— If you paint over the scratches and stray pencil marks with ink, it will probably cover it up and not show.  You should try this on a scrap piece of paper first, to be sure.