There are no exact answers to these questions because different things can affect the results. What will grow under one black walnut may not grow under another with different conditions.

The site in the link below may be helpful in recommending plants that are generally considered Juglone Tolerant.

Roots of a mature black walnut can extend in excess of 100' in all directions from the trunk of the tree. There will be less and smaller roots the farther you go from the trunk, so the effect of Juglone should decrease as the distance from the trunk increases.

Here is a link that might be useful: Juglone Tolerant Plant List