Impossible to answer. By definition, rectangles are only two dimensional.
By extrapolation...
A three dimensional rectangle would be a rectangular cube; this would have six planes.
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A rectangle is a 2-dimensional (plane) object while a cuboid is 3-dimensional (solid).
A 3 dimensional rectangle would be a rectangular prism.
A rectangle is a 2-dimensional figure. 2-d figures do not have volumes, which is a 3-dimensional concept.
Yes, it's not 3 dimensional unless it is a box. Everything that is flat on paper is 2 dimensional.
A vertex is a point and so does not have any sides. In 2-dimensional space, there must be at least 2 lines meeting at a vertex and in 3-dimensional space, there must be at least 3 planes.