A plane figure is 2-dimensional.
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There are infinitely many different plane figures that can be made up of 2-dimensional shapes - provided that they are all in the same plane. There cannot be any 3-dimensional shapes involved.
Because they are both 3 dimensional
2 dimensional (plane) figures can have three or more straight edges as sides. 3 dimensional (solid) figures can have four or more plane sides (faces). They can have fewer sides if the sides are not straight.
A 2-dimensional (plane) projection of a 3-dimensional (solid) figure. Or, for polyhedra it could be a net but that answer would not be applicable to many 3-d figures.
An object cannot be 3-dimensional and plane at the same time since the term "plane" refers to 2-dimensional objects, such as geometric figures drawn on a sheet of paper. However, certain 3-dimensional objects, for instance a cube, are comprised of 2-dimensional (plane) figures (in this case, 6 of them). On the other hand, a sphere has no plane faces (but theortically approaches an infinite number of them) since no aspect of a sphere can be truly represented on a flat (plane) surface. For practical purposes though, each tiny portion of the sphere could be thought of as a plane figure, and a perfect example of this is a road map.