An octahedron is a closed 3-d shape with 8 polygonal faces. There are 257 topologically different convex octahedra. Some of these have no parallel sides whereas a right hexagonal prism has 3 quartet of parallel sides and one sextet.
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It can, but it need not have parallel lines.
The 12 edges of a regular octahedron consist of 6 parallel opposite pairs. In fact, the 12 edges form 3 squares.
Infinite
There are 257 topologically different convex octahedra. Many of these will have no parallel faces. It can have four pairs of parallel faces.
how many sets of parallel lines are in a triangle