Re: How could one make a fuel cell out of chlorophyll?

The answer to your first question is 'no'. A fuel cell is nothing more nor less than a means of converting chemical energy directly into electrical energy. It uses a fuel. However you carve it up, the only abundantly available high energy chemicals are those containing carbon, that have been generated as an energy repository as a direct or indirect result of photosynthesis. And when these chemicals are consumed, even in a fuel cell, carbon dioxide is produced.

That is not to say that carbon is always involved in fuel cells: hydrogen/ oxygen fuel cells have been well developed and widely used in specialized applications. But the hydrogen fuel must be generated in some other way from high energy chemicals. The cheapest and most efficient means of producing hydrogen at present is by steam reforming of natural gas -- it beats electrolysis of water by a country mile!

CH4 + H2O ---> CO + 3 H2

The reaction, as you can see, does not look very environmentally friendly.

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Now let's look at your questions about chlorophyll.

Any colour of light has a vibrational frequency associated with it. To get the frequency you divide the speed of light by the wavelength of the light. The colour that matters is not the green light that is reflected by chlorophyll, but the red light that is absorbed: that is the source of the energy that chlorophyll uses. The fact that green light is reflected means that its energy is being turned away for the rest of the universe to use, if it will.

wavelength of red light is about 650 x 10^-9 metre
speed of light is about 3 x 10^8 metre/second

therefore frequency is about 4.6 x 10^14 Hz, or 460 THz.

This is a frequency that is too high to be mechanically reproduced. But what you would achiveve by mechanically reproducing it is unclear. What you are really trying to do is to artificially trap the energy that is in the red part of sunlight like chlorophyll does. And any green dye will do this; it does not have to be chlorophyll.

The important point about chlorophyll is not just that it can trap the energy in red light, but that it can use that energy in two of the steps of a cycle of biochemical transformations, that eventually have the nett effect of producing glucose from water and carbon dioxide. I recommend Chapter 4 of E.J. DuPraw "Cell & Molecular Biology", Academic Press, 1968 for a readable discussion of the chemistry and energetics of photosynthesis.

With regard to your last question, it is important to remember that animals and many microorganisms do not photosynthesize, and must find high energy chemicals outside themselves for their energy supply. Thermal vent 'plants' are no different in this regard. There are opportunities for obtaining energy from chemicals emerging from the vents.