electricity from gas?

I don't want to be "that guy" but I have very little knowledge and NO experience with this kind of thing.

Say for example that I create an anaerobic digester to generate biogas. Say I figure out how to build it correctly, and it's functioning optimally.

1. Is there some sort of way of calculating what volume of gas it will produce, and at what rate?
I'm reading Rob Hopkins book, The Power of Just Doing Stuff, and in it, he talks about a place where there are gas lanterns powered by pet waste, which sounds cool, but then he talks about how some lamps have been redesigned to power LED bulbs instead of burning gas, and I'm stuck trying to figure it out.

2. I understand that I can burn it for heating, cooking, lighting, etc. but how do I use it to power a light bulb or charge a cell phone?
3. Doesn't the conversion of energy from one form to another carry some sort of entropy-effect making it less efficient or something?

Would appreciate some insight, or some helpful links or videos.

From my research into biogas digesters scale is really important - if your waste stream is just material from a normal household you might have enough gas to cook some meals, but you won't have enough surplus to run a generator etc... If you have a dairy farm and lots of cows crapping in the dairy house then you can work on a larger scale and probably provide meaningful power to a whole house.

I have seen folks power trucks and tractors with wood gas, I am wondering if you could do the same thing?

If you can power an engine you should be able to turn a generator , right?

Yes, you can run a generator, again, based on the volume of production. You may also use LP lamps, And there are also freezers and refrigerators that run on LP gas.

Raw biogas is (primarily) about 55% methane and 45% carbon dioxide (in the details, there are small amount of other chemicals like hydrogen sulfide, which needs to get cleaned out). It can be burned at relatively low energy value per unit of volume directly, and so works well for cookstoves, water heating, and can even be burned directly in a low power engine. The carbon dioxide lowers the by-volume usefulness of the biogas as a fuel. In a standard ICE engine, the amount of fuel that can be burned at once is limited by the displacement of the engine (specifically the cylinder), and don't forget to leave room for the oxygen. Carbon dioxide won't burn, so it's just taking up space. Woodgas, on the other hand, is primarily a blend of carbon monoxide, which will burn, and hydrogen, which also will burn. So, blend in some oxygen and the whole volume of gas is a fuel. Since the process of creating woodgas involves airflow, the oxygen is already there, so it's pre-blended and ready to go.

Raw biogas can be cleaned to remove impurities (H2S, water, etc.) with relative ease. Removal of the CO2 is a little more difficult, but not horrible. If you use a water scrubbing system, you evidently end up with 96% methane, which is "vehicle grade".

I know I'm late to the party with this, but I hope it helps.

Cheers.

JD