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Square
Yes you can draw the nets of 3D objects on graph paper
no. a 2d square has only 1 face but a 3d square (cube) has 6 faces.
The following are some shapes having a square cross section: a cube, a cuboid, a square pyramid.
The special features of 3D shapes are they all are 3D which means they are fat but 2D shapes are flat they can not stand up.