Hyperbolic plane geometry is also the geometry of saddle surfaces and pseudospherical surfaces, surfaces with a constant negative Gaussian curvature. A modern use of hyperbolic geometry is in the theory of special relativity, particularly Minkowski spacetime and gyrovector space.
It depends on what you are talking about when you say "create the look".
Most likely, the answer you are looking for is the Director, because the Director will give input to the costume designer on the character's look and how it fits into the overall design elements of the entire production.
If, on the other hand, the question is asking about who assists in building the costumes, then the answer is the Wardrobe assistant.
Again, it all boils down to if "create" means design or construction. In context, my best guess is it's referring to design, in which case the answer is the Director.
A loose dress.
One careless move and that lathe will have her all tangled up in all sorts of ways. In fact, she'd be wise to dress in Jeans or attractive slacks, and a blouse that's neatly tucked in at the waist. She would also be wise to make sure she is buttoned up and that there are no loose ends anywhere. Lathes look harmless, they are just like any other machine; care must be taken when working on them.
The only worse thing she could do would be to be careless around a band saw or a table saw.