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It is a rectangle which is similar to the base.
It is a rectangle which is similar to (but smaller than) the rectangular base.
A prism can have a triangular cross-section with a rectangular base
A circle.
It depends on the pyramid. If it is a square based pyramid, a horizontal plane will give a square cross section, a plane inclined by a rotation parallel to one of the base axes will give a rectangular cross section whereas a plane inclined by rotation along both basal axes will result in a parallelogram cross section. Not sure how you get a parallelogram from a pentagonal or hexagonal (etc) pyramid.