You cannot have a 2d pyramid - whether or not it is square based. The 2d cross section will depend on the plane of the cross section.
The following are some shapes having a square cross section: a cube, a cuboid, a square pyramid.
Depending on the inclination of the plane used for the cross-section, it could be a square, rectangle, trapezium, triangle.
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.
The cross sections of a pentagonal pyramid can vary depending on the orientation and position of the cut. If the cut is parallel to the base, the cross section will be a smaller pentagon. If the cut is vertical and intersects the apex, the cross section can be a triangle or a trapezoid, depending on where the cut is made. Other diagonal cuts may produce various shapes, including trapezoids or quadrilaterals, depending on their angle and position relative to the pyramid's structure.
triangle
You cannot have a 2d pyramid - whether or not it is square based. The 2d cross section will depend on the plane of the cross section.
a square
a square
The following are some shapes having a square cross section: a cube, a cuboid, a square pyramid.
a square
Depending on the inclination of the plane used for the cross-section, it could be a square, rectangle, trapezium, triangle.
It can be a square, a trapezium, a quadrilateral or a triangle - depending on the inclination of the plane which defines the cross section.
square pyramid
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.
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.
cone, cylinder, rectangular prism, square pyramid and triangular prism