For instance, "the color of the watermelon is red and green", or should one say "the colors of the watermelon are red and green"?
the color of the watermelon is red and green
Is technically incorrect, but widely accepted and understood. One could also say more simply
The watermelon is colored red and green
or even just
The watermelon is red and green
since those will be understood as colors.
The watermelon is green.
could mean that it is unripe, rather than green in color.