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I think WinBoard uses the bitmap for the entire board, or tiles it if the
bitmap you have given is not big enough to cover the entire board. I did
not code this part myself, so I cannot give you the details off hand.
There are additional options /darkTextureMode and /liteTextureMode that
control if some additional randomization is done in the process of cutting
the squares out of the given bitmap. I am not sure how this works exactly,
I hardly ever use the texture modes, as I like evenly colored squares
better.

Fonts are better than bitmaps, because the bitmaps cannot be scaled. So
for every board size you would have to remake the bitmaps from scratch.
The font can be rendered at any size.

Fonts are indeed pure black/white constructs. The black defines the
outline, and any internal areas are filled with another color to get a
shading effect. The colors and shading are user-selectable. I am not so
sure about the desirability of having multi-colored pieces (on top of
outline and two colors for defining the filler shading gradient). It seems
to me that this would only degrade the ease of recognizing which side the
pieces belong to.