Yes, it is.
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A pentagonal pyramid.
A pentagonal is not a shape. You an have a pentagonal pyramid, a pentagonal prism or a pentagonal polyhedron as well as other shapes - each would give a different set of answers.
It is a polyhedron with a pentagonal base. To every side of the pentagon are attached triangles that meet at a single point in a plane higher than the pentagon (if it is a skew pyramid, the apex will not be above the pentagon).
Yes.
A six sided polyhedron is a hexahedron. This may be a triangle based dipyramid, a pentagonal pyramid of a variant of a parallelepiped.