I would say yes on both. As far as I know there is no law prohibiting anyone from sitting out in the field public or private without a weapon. I would recommend him wear hunter orange just for safety's sake.

As far as the trapping question goes. As long as he isn't actively assisting you in anyway, then I can not for any reason see how he couldn't tag along. If he is interesting in learning how to trap, then I think it would be a great learning experience for him.

I am not a lawyer and I did not stay in a Holiday Express last night. This is just my humble opinion.