1.
A free body diagram is one of the most important tools used in the Newtonian mechanics part of physics. It is a diagram that shows all of the different forces that are acting on a body. An example of such below.

                     ===========
         F1---> =                |   =
                     =     ^N      |   =
                     =      |     G v   =
                     =      |             =<--- F2
                     ===========

Locations are approximate
The forces would then be reduced into x and y components (here they are only in 1 direction anyway, so it doesn't matter) They are then summed and conclusions are made. For example, since the normal force and gravity are equal on this flat surface, there is no y direction acceleration. If F1 were bigger than F2 then there would be acceleration in the direction of F1 corresponding to the net force and the mass of the box, and vice versa.

2.
A free body diagram could in theory also be a drawing of something that you don't have to pay for.

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