What fossil fuel may be found on a carbon planet?

Well oxygen is toxic and corrosive here, too. ;) It is also not flammable/combustible on its own. It can support combustion, yes. But pure oxygen in a pure oxygen environment isn't combustible as I recall.

Anyway, the extraction of oxygen from carbon monoxide is something well within the range of 19-20th century tech. The basic reaction process, known as hydrogenation, is to combine it with hydrogen and a metallic catalyst. This is a strongly exothermic reaction that produces ethylene and water. From there you can separate the water via electrolysis or via algae reactors.

An algae reactor leverages the fact that certain algae, when they are deprived of sulfur, switch to making hydrogen from water instead of oxygen. It could be that on your world certain algae naturally do this. That could make for interesting geopolitical situations as well as interesting terrain features where such algae is present. While you don't get oxygen directly from the water, it is low power and produces hydrogen which is very valuable for many of the reactions I'll mention.

Of course, you could still have algae which split water into oxygen for you, too. So perhaps you have a bioreactor for each, with the oxygen and hydrogen coming off of it being used as inputs various chemical reactions. And while we've only recently figured out the sulfur deprivation trick, we've known about the hydrogen switch for over a century so even that should fit the tech level given.

For example, I can envision a steampunk algae bioreactor setup combined with an ethylene generator, with the heat from the ethylene/water generator producing electricity turbines via low-level steam turbines. You'd also thus have ethylene which is a pretty decent fuel - and could serve as a foundation for the beginnings of plastics production as well as a liquid fuel. Perhaps your world is more plastic than metal based? The production of polyethelyne on our world consumes about half of our prodigious production of ethylene.

We first started knowingly mucking around w/ethylene in the 1600s so it fits the tech level you gave. The catch is is is essentially a bit energy intensive to make. Of course, ethylene is a hydrocarbon, and it may also occur in deposits on your world in the way oil does on ours. Rather than decomposed dead things, they might conceivably form underground where CO, water, and algae were trapped. Or maybe you've got an algae that does it not from photosynthesis but from thermal energy. Then you could have "pockets" of ethylene underground (or near thermal vents) - perhaps from tectonic shifts which brought the algae and water down into the ground.

As far as ethylene as fuel, for heating it is about 5 times more useful than carbon monoxide directly (yes, CO can be used as a fuel). If your industries have access to chlorine they can also use it with the CO to provide a stepping stone to various acids.

I've also seen some references to using a copper catalyst to break out the oxygen from carbon monoxide but don't know the particulars. There are also references to using zirconia to electrolysis to produce

As for CO directly as a fuel, this paper from 1949 talks a bit about CO uses as a fuel, comparing to methane. Note that most of the paper is about actually producing the CO, which may not be an issue on your world. ;) Also, you can relatively easily mix a catalyst, CO, and H2 to produce methane as well. For more ideas on that you could also check out this article which talks about coal gas - which contained CO as a key component. For gross and net heating values per cubic foot or per pound, CO is about as good as H2. Note that ethylene is still loads better by volume, but less than hydrogen by weight.

That said, I guess "common" may need more clarification. Carbon monoxide is combustible and has a lower flammability level of, IIRC, around 12% and an upper limit of about 75% - so it better be really common or not that common. ;) So really, provided you have a means to dilute/concentrate the CO found in the air you've got fuel to burn and thus bootstrap other fuels.

Other bits to look up would be the Water-Gas-Shift, Sabatier reaction, and Reverse-Water-Gas-Shift to get more details on ways your planet's industry could develop fuels.

Now as to your carbide rich surface, this can produce fuel for you "naturally" as well. You could have methane and/or hydrogen pockets (from water+beryllium or water+manganese carbides), for example. There are additional possibilities such as acetylene, ethylene and various mixes. That said I'd feel free to stipulate that the planet isn't "carbides all the way down".

Hopefully that provides you with some options and ideas.

Oxygen isn't the only thing that will support combustion. There's also chlorine, fluorine, and various non-elemental oxidizing agents like sulfates, nitrates, chlorates, and the infamous FOOF and chlorine trifluoride.

Some of those, like sulfates and nitrates, might reasonably be naturally produced, either by biological or geochemical processes, and could be mined as solid fuels, analogous to coal.

Ancient lifeforms might also produce energy-rich molecules that do not require combustion / reduction at all, but release energy by simple decomposition, like nitroglycerin.

And since water reacts exothermically with carbides directly, why would you need or want to extract oxygen from it? That just makes it more difficult to work with. Just use water + carbide rocks as fuel directly.

Extracting oxygen directly from CO seems non-trivial; at least, I couldn't find any information on how to do it in 10 minutes of casual research. It might be easier to first decompose CO into carbon and CO2, and then separate the CO2, possibly by electrolysis. Honestly, though, there doesn't really seem to be much point in that. EDIT: While there are more steps involved, the hydrogenation process described in The Real Bill's answer is probably more suitable, especially for the given tech level. Still, though, I don't really see the point in it.

I actually wrote a novella about a similar planet! In that story, some animals extracted oxygen from the air and stored it as a liquid in pressurized organs. Perhaps the biosphere on your planet does something similar, storing oxygen in some stable form that can be broken down when needed (the way plants store sugars). If you get enough organisms doing that, and they're buried and fossilized, you get deposits of oxygen-based fossil fuel.

I'm not sure what the chemistry would look like, though.