It's called, not altogether surprisingly, a hexagonal prism. If the bases were hexagons and the other faces were triangles, it would be a hexagonal antiprism.
If by faces you mean sides, then lots. Parallelograms and squares come to mind but I'm sure there are more (hexagons for would be another).
The 3d shape that have five faces would be a triangular prism **************** or a pyramid
A hexahedron is a three-dimensional figure with six identical faces - in other words, a cube. So a hexahedron is not made up of hexagons at all, but of squares. However, if you were to balance a cube on one of the vertices, the horizontal plane cutting the cube in half would make a cut in the shape of a regular hexagon. Four such regular hexagons can be found in the cube.
I would mostly say yes if it was a cube but I don't know
If by "vertex," you mean "apex," than any pyramid would fit the description.
Honeycombs are made up of hexagons, so I would say a hexagon.
Since a cube has 6 faces, you would be looking for a solid shape with only 2 faces and no such solid exists.
the other faces on a pentagonal prism would be rectangular
Its a Octagon * * * * * No. An octagon is a shape with 8 sides. 8 faces implies a 3-dimensional object, which would have to be an octahedron.
Assuming the shape is a simply connected polyhedron, there are 6 faces. A triangular dipyramid, for example.
The shape you're looking for that has 2 faces, 0 edges, and 0 vertices would be a cylinder.