This comes pretty close to being a duplicate of Biochemistry of a sulfuric acid world?, but specifying that the creatures here breathe fluorine is a large enough departure that I suppose it warrants answering separately.
their planet is a carbon planet dominated by carbon based geology with
very little oxygen
In that case, there is almost certainly a lot of carbon tetrafluoride around as well, and plenty of carbon as a heteroatom in the siliceous biochemistry.
If you have oxygen in the biochemistry (which you do, as part of H2SO4 at least), you will also probably have some free oxygen in the atmosphere, because fluorine will displace it from pretty much everything. Oxygen may thus end up serving a similar role in biogeochemical cycles as nitrogen does in Earthling biology--it has to be fixed out of the air into silicorganic forms for use as a heteroatom.
I am also very skeptical of the plausibility of maintaining significant quantities of atmospheric F2 at 400F... but we'll do the best we can!
As a carbon planet, you'll have a lot of silicon carbide minerals, in place of the usual silicates (silicon oxides). One usually expects that to result in a much more rigid geology... except in this case, it can be attacked by hydrofluoric acid! Some polymorphs of silicon carbide (e.g., α-SiC) are essentially immune to acid attack, but others break down rapidly, producing SiF4, CF4, and hydrogen gas. The surface minerals that survive will be fluorine-terminated, much like the surfaces of silicate rocks are hydroxyl-terminated on Earth.
so, how could things like chemosynthesis work in this environment?
Well, there's the "chemo-" part, and then there's the "-synthesis" part. The "-synthesis" part is reusable, so let's focus on the "chemo-" first.
Plenty of chemical energy sources that are used on Earth should still be accessible to life forms on this planet--oxidation of metals, reduction of oxidized substrates (e.g., methanogenesis), etc. But there are a couple of unique processes that your world's organisms could catalyze, and in the process help transform a primitive world with an inert atmosphere into the modern world where things breathe fluorine.
Sulfate ion exchange. Organisms immersed in sulfuric acid solvent and with access to halogen salt-containing minerals can gain energy by extracting halogens to produce hydrofluoric and hydrochloric acid and depositing sulfate minerals in their place.
Silicon Carbide decomposition. Where sufficient quantities of HF are available in the environment, organisms can catalyze the decomposition of SiC into SiF4 and CF4, producing waste hydrogen. Symbiotic methanogens could then convert additional SiC, or partially-oxidized silicorganic substrates, into methane and elemental silicon (and probably some extra regenerated HF as well), and additional layers of organisms (or perhaps, sometimes, the same organisms--horizontal gene transfer is a wonderful thing!) can then convert elemental silicon and HF into more SiF4 and hydrogen, and so on. (Methane will of course burn in F2, just as it does in O2, but it's inert against reaction with H2SO4 and HF, and primitive anaerobic methanogens can be expected to survive into the fluoro-aerobic age just as they have survived in anaerobic environments on Earth.)
Carbide-decomposers have a nice leg up on sulfate-exchangers, in that their energy production process will also produce useful biosynthesis inputs (unsaturated fluorosilicons and fluorocarbons) as intermediate steps. Sulfate-exchangers would need environmental access to structural-food molecules as well as energy-food molecules--which is not unusual for extremophilic Earth bacteria, and it's perfectly suitable to an abiogenic environment where proto-lifeforms are assumed to be assembling out of a soup of non-biologically-produced components anyway.
Now, what would primary producers actually be synthesizing, whether they get their energy from chemical reactions or capturing photons?
Given the environmental prevalence of silicon carbides, and the relatively low accessibility of oxygen (yes, you can rip it out of H2SO4 with a lot of energy, and eventually it will be accessible from the atmosphere, but none of that will be true in the early days when basic universal biochemical pathways are being established), I would expect some kind of partially (or even fully) halogenated polycarbosilane as the rough equivalent of glucose (as opposed to polysiloxanes, which would be expected from an oxygen-rich silicate world). E.g., some derivative of 1,3,5-trisilacyclohexane, or Si3C3H6, where some or all of the hydrogens are substituted with other functional groups that make it more stable against fluorination and provide active sites for polymerization and manipulation by enzymes--e.g., most hydrogens could be substituted by fluorines, chlorines could stand in for polarizing hydroxyl groups, and difluoromethyl groups (-CHF2) could stand in for reactive hydroxyl groups permitting polymerization by defluorination rather than dehydration. In general, you can expect to see partially-saturated carbons in this environment standing in for reactive oxygens in our lower-temperature, water-based biology. When oxygens do end up incorporated into biochemistry, they will either be part of siloxane polymers & rings (providing a stronger bridging bond between silicon centers than carbon can), or as part of polyatomic ions, like sulfate and phopshate.
Fluorogenic synthesis would most generally proceed by cracking SiF4 and CF4 to produce SiF2 and CF2 radical units, with splitting of HCl and HF for hydrogen to use to attack the relatively inert terminal fluorides as an internal process which is the actual source of free fluorine gas, much like water cracking for hydrogen is an internal process in Earthling photosynthesis, even though the big-picture photosynthesis equation makes it look like oxygen is being removed from carbon. Exactly how much fluorine is released in the photosynthesis cycle would depend on just how much hydrogen actually ends up incorporated into the structure, vs. how much the carbosilanes remain perfluorinated and how much hydrogen just ends up being used to regenerate HF.
