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The cross section of a cuboid box, bt a plane at an angle to all of its sides will be a point, triangle or quadrilateral - depending on it location. The cross section by a plane perpendicular to an axis of the box will be a rectangle.
Yes
If it's just the front surface of a box then it's simply a 2D shape, the area can be calculated by multiplying the length by the width. Answer will be in units squared.
because the friction involved in the box sliding down has overcome the pull of gravity.
The front surface of a box is a rectangle. If you only need the area of the front surface, then it doesn't even matter what it's part of. Multiply the width of the surface by its height. The answer is its area.