They can come in any order.
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Either doesn't really matter.
Well, first of all, you don't need to be given the height, width, volume, and length. If you're given any three of those numbers, you can calculate the fourth one. To answer the question: -- If the thickness of the box can be neglected, then the height is also the depth. -- If the thickness can't be neglected, then even with all that information, I still don't think you have enough yet to determine the interior depth.
Depends on the depth of the box (or the height). If the box is 16" deep, then it would be 12x10x16.
whichever you like, its a Cube, all dimensions will be the same. however if you weren't asking this as a trick question then its Height x Width x Depth
Yes - in the US we use an industry standard called the modular system which places all dimensions of building products in the same order - width, height, depth.