Biomass can be turned into Methane via an anaerobic digester. Just add water and bacteria to biomass and exclude oxygen. Its the most efficient biofuel. The bugs are self powering and reproduce the only catch is that you must balance the nitrogen to carbon ratio to about 20:1 carbon/nitrogen. That’s easy add urea, urine or manure.

Biogas results: that’s a mix of methane and CO2. Its incompressible because of the CO2. Scrub that out with lime and you have natural gas.
An catalyst and refrigerator will turn methane into ethane. The reactions are all exothermal but the biogas digester must be kept warm to work. Insulation in higher latitudes will do; heaters are required above the Arctic circle. The ethane reaction is used in industry to heat and drive other reactions. Ethane can be used in cars with a pressure tank, adding a little propane and chilling a little increases ethane’s usability. The mix gels in the tank reducing pressure concerns.

Fischer–Tropsch Synthesis can be used to make oil but its several steps backwards to go forwards and you have less control of the products. Adding in methane or ethane to the Fischer–Tropsch Synthesis increases the productivity and control. There are other pathways that allow heavier hydrocarbons to be synthesised direct from methane and ethane mixes. Some resemble fuel cells.

So far no energy input is needed up to ethane.
Heat and electricity from the the Focus Fusion unit would be used to cook the limestone mud that results from the lime wash of the biogas back into lime. This regenerates the lime. Heating ethane under pressure with a proton conductor or catalyst makes the heavier hydrocarbons. The catalyst strips off a few hydrogen atoms and the carbon carbon link form making a longer chain hydrocarbon. Catalyst type and geometry governs the Octane number or level of branching in the hydrocarbon result.

These processes produce hydrocarbons that need need less refining than crude oil but it will need some. Heat and power from the FF unit could drive the refining. Often oil refineries are powered by running the heavy oils and tars through a furnace and burning them. A FF biofuel system and refinery would produce very little tar so the power from the FF unit is needed.

To be viable you will need more than one chemical pathway and catalyst combination out of your methane ethane stage. Most fuels are a mix of hydrocarbons and related compounds so if you don’t want huge flammable storage you will need simultaneous parallel production of the mix.

A focus Fusion unit can also provide heat and power to refine cellulose for celluloseic ethanol and to heat the stills. It can also power illumination of seals vats of algae oil and refine the product.

It should be noted that there is a way to make alcohols and sugars and even protein from the Methane ethane mix. Add Carbon monoxide in the presence of the right catalysts. Its very very energy hungry and the sugars are pretty basic but If we have fusion we can make food in theory. However simply powering a greenhouse or hydroponics unit will work better and produces much more variety.
With unlimited energy at a low price you can do it all.