If we go by the information provided by the supplier, it's highly likely that the answer is yes: "...hard spices such as nutmeg, cinnamon, Tonka beans, long pepper, different varieties of walnut and much more. Grating hard spices has never been easier or quicker...".

Should work. I can test it for you if you send me some dried ginger :-)

Coriander seeds might work (a bit coarse?) but cumin seeds are too small in my opinion. I haven't tried it though. I prefer to grind cumin.

Yes, there is a lid at the bottom. We always keep the nutmeg in the grinder and no crumbs fall out.