Rhombus
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Two pairs of touching sides are the same length. The diagonals meet at right angles. Opposite sides are not parallel.
A two-dimensional shape (polygon) is said to be "regular" (or equilateral) if all its sides are the same length and all its angles are the same angle. A regular pentagon, for example, has 72-degree angles on all five angles, and all its five sides are the same length.
A rectangle has 4 sides not the same length and 4 right angles.
When the 3-d shape is a prism and the cross section is in a plane at right angles to the length of the prism.
In a real star, no. In a 2-dimensional star-shape, no. In 3-dimensional star-shapes, yes, there can be.