You have me stumped. On an E6-b, the procedure is to line up "fuel lb" or "oil lb" on the outer scale with a liquid volume (e.g. US gal) arrow on the inner scale. This way you can find your fuel or oil quantity around the inside and see how much it weighs on the outside.

By the looks of it, the Nighthawk's dial is missing the necessary markings on the inner bezel for the calculation, but it has all of the necessary markings on the outer dial. I suppose if you find the fuel or oil markings on the outer bezel and lined them up with 12.8 (corresponding to US gal) on the inner bezel, you could still do the calculation...but you might as well just multiply at that point.

I suppose I'll have to buy a Nighthawk to try to figure it out

To help with your other question, aside from picking calculations out from an e6-b instruction manual, the only thing I would know is to look up instructions for a regular slide rule. An e6-b is just a specialized slide rule made more convenient for cockpits. The scales on the bezels of a slide rule watch are just like the logarithmic "C" and "D" scales on a slide rule. These scales were designed primarily for multiplication and division, so calculations that involve multiplying by a conversion factor (eg. currency or length conversion) or using a ratio (eg. miles, hours, and miles per hour) will work.

As of now, what all do you know how to do with it?