Yes.
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No, but a pyramid is.
A pyramid, as well as any other solid figure bounded by plane polygons or faces, is a polyhedron.
Yes. A polyhedron is a geometric shape with flat surfaces and straight edges, so a a pyramid with a rectangular base qualifies as a polyhedron. It is however not a regular polyhedron, which would require all the faces to be the same shape and size. To change your pyramid to a regular polyhedron you'd have to turn it into a tetrahedron.
Yes, it is.
Yes because it has many faces which is the meaning of a polyhedron