Does this set come with a case to keep them in?

No case. I keep them in the original plastic tray in the box. A case would be nice. Good idea.

Is the toenail clipper a curved or straight cut?

The No-mes toenail clipper is very slightly curved (almost straight). For clipping toenails its best leave the corners of the nails slightly longer to prevent ingrown nails. Clipping toenails with too much curve could cause the nail to dig into the skin and could result in an ingrown nail.

Is the steel used to make these clippers American steel?

The stainless steel used to make the No-mes nail clippers was purchased in the USA from an American company.

Can you use the big one for finger nails?

I would say based on the size of your nail bed, it would be to your preference and/or discretion........the toe nail clippers do have a larger opening, so when using any nail clipper or toe nail clipper, always use them with caution.