Its called a net.
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It is a polyhedron.
Nope - A polygon is a flat, 2-dimensional shape. A Polyhedron is a 3-dimensional shape.
A face
No. A triangle is a two-dimensional polygon (flat figure). It has sides that consist of three line segments, with an interior area. Only a three-dimensional form (polyhedron) can have faces. Triangles serve as faces for any number of polyhedrons, such as pyramids.
If you're thinking of a polyhedron like one of the platonic solids, then I believe the faces are called "hedra" or "hedron" singular.