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In 2-dimensions, it is the y-axis. In 3-dimensions, though, the x and y axes form the horizontal plane and the z-axis is the vertical axis.
I believe it is horizontal by vertical. (example: 12x24)
Area = 2*vertical height
That's really going to depend on the height of the 500bbl vertical oil tank. We could also calculate the answer if we knew the shape and dimensions of the floor of the tank, but you haven't included that information either.
You can add vectors graphically, by drawing them head-to-tail. Algebraically, you can separate them into components (for example, in two dimensions, the horizontal and the vertical component), then add those.