An irregular polyhedron is a solid shape in which either all edges are not the same length, or all faces are not congruent polygons or all [solid] angles are not of the same measure.
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A regular polyhedron (other than a hexahedron), any pyramid, as well as most irregular polyhedra.
Some do, some don't. A regular polyhedron such as the tetrahedron has none whereas an irregular one like the parallelepiped can have several.
yes it is a polyhedron
A pyramid has a polygonal base with all other sides being triangles. As the Egyptians famously demonstrated, a common pyramid has a square base with four triangles meeting at a vertex, but any polygon - regular or irregular - can be used as the base of such a polyhedron.
no a cuboid is not a polyhedron if it was it would have 9 faces