Well, I can't offer you much advice on how to make the green cloak since I haven't made one myself. I plan on making a Young Nel next year and my plan was to purchase a yard or two of green fabric and just sew it since the costume is quite basic. I wish you luck with making/finding it though.
As for the wig, I plan on purchasing this one and therefore highly recommend it:
I believe it has just the right amount of turquoise and green since her hair transitions from those two colors multiple times during the series and it's quite affordable.
I wish you luck in the production of your costume!