It is a rectangle.
It is a rectangle which is similar to (but smaller than) the rectangular base.
The vertical cross sections are trapezia or triangles. The horizontal cross sections are rectangles which are mathematically similar to the base.
A triangular prism has a uniformed cross-section whereas a rectangular pyramid does not.
A prism can have a triangular cross-section with a rectangular base
A rectangular prism has the same cross section throughout its length, a pyramid doesn't however
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.
A rectangular prism has a rectangular cross section whereas a cylinder has a circular cross section
A cylinder has a circular cross section, a rectangular prism has a rectangular cross section.
cone, cylinder, rectangular prism, square pyramid and triangular prism
The vertical cross section of a right vertical cone is a triangle if that cross section is taken from the vertex. Any other vertical cross section will reveal a hyperbola (with endpoints on the base of the cone). A link can be found below.