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There are 29 distinct pentominoes in three dimensions. 5 pairs of them are mirror images and can be rotated in 4-space to be considered the same. There is one 4D pentomino that cannot be built in 3D for a total of 24 4D pentominoes.
they all tessellate because they all fit together
There are 18 if you count mirror images as distinct; 12 otherwise.
Yes. URL: http://en.wikipedia.org/wiki/Polyomino#Tiling_the_plane_with_copies_of_a_single_polyomino
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