No
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A sphere.A sphere.A sphere.A sphere.
A sphere cannot be stacked tightly together. (It can't tessellate) A cube for example can and therefore maximizes storage space.
Regular pentagons will not tessellate but there are 15 classes of convex pentagons – the latest discovered in 2015 – which will tessellate.
Yes, you can.
None. It is not possible to make a sphere in that fashion.