Yes.
Probably. It depends on what other genes the NZW has. For example, you would not see white spots on a white rabbit, but you would see them on a sandy rabbit.
But I think Sandy offspring would be the most likely.
I had to go look it up, but the difference between fawn and sandy is mostly caused by one gene. So if your doe Nutmeg has that gene, she will pass it to about half of her bunnies, and breeding her to one of her sons could produce some fawns (if he's one that got that gene.)
Did you see Nutmeg's parents? If one of them is fawn, then she must carry the correct recessive gene. (With 4 fawn siblings, it is likely that one parent is fawn, and the other a sandy carrying the recessive gene.)
Breeding her to a fawn buck would also work, but you don't have one of those right now.