A regular heptagon (or septagon, if you prefer) has seven equal sides and seven equal angles, and none of the sides is parallel to any other one. There is a bit more.
There are an infinite number of other (irregular or non-regular) heptagons that may have at least one pair of parallel sides, and an infinite number that do not have any sides that are parallel.
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There is no such shape. There is a heptagon (7-sides) or an octagon (8 sides) but not hectogen!
A rectangle is a shape that has four sides with two parallel lines.
None. A parallel is not a shape and so does not have any sides.
square
Any polygon with four or more sides can have a pair of parallel sides. It is also possible to to have non-polygonal shapes - eg a cigar-shape - that has parallel sides.