Is it possible to have a cellular metabolism based on reduction instead of oxidation? All known life currently uses some sort of oxidation in cellular respiration, either from oxygen or from oxidizing Fe2+/other chemosynthesis
Any oxidation reaction is also a reduction reaction; at least one reactant is oxidized, and at least one reactant is reduced.
Here on Earth's surface, most animal life eats its reducing agents, respires its oxidant, and excretes reaction products in solid, liquid, and/or gas form. I don't really think of myself as an "oxygen-reducing organism", but it's a fair characterization.
I can certainly imagine an organism that eats its oxidants and breathes in a reducing agent, or eats or drinks both agents -- Oh, look, they already exist!
Oxidation reactions bring the atoms involved in a configuration of lower free energy, therefore they are energetically favored and lead to the release of energy, which life can use.
Reduction reactions instead bring them to a higher free energy configuration and absorb external energy. Since the purpose of metabolism is producing energy for the organism, this would be a dead end.
However parts of the metabolism can be reductive: for example the photosynthesis is a reduction, which allows the plant using it to store solar energy into sugars which can be later used.
A tail of two fluids
What is a hydrocarbon world like?
There are methane lakes on Titan. And rain and rivers! But water is actually more abundant on Titan: just dig a hole and once you get past the hydrocarbon and thiolin muck you will hit water. In the tropical deserts you don't even need to dig: there are plenty of dry, rocky plains which are mostly made of water. Bring a pickaxe.
Hydrocarbons and water are also abundant in Gasoline world. But it's much hotter than Titan and most of the water is melted. Methane and ethane are potent greenhouse gases that make up for Mars-levels of sunlight. The oil seas are hydrocarbons that generally weigh 5-20 carbon atoms per molecule. They float as meter-thick slicks over most of the ocean.
On Gasoline both oil and water can evaporate and rain down: waves and currents will disrupt the slicks and let the water escape. Oceans are saltwater, but rain is freshwater. And ocean slicks are waxy oil but rain, rivers, and lakes are clean oil (which won't leave a residue if it evaporates). Some rivers flow with water (laced with benzene and other stuff). Others are oil. But most are mixed flows: ranging from a sedate bilayer to a torrent of salad dressing.
Feast on the nitrate
There is plenty of gasoline, but no oxygen to burn it with. On Earth plants must make do with CO2 as a source of carbon, expending energy to wrench the "C" (as glucose) from the "O2". On Gasoline they have much easier sources of carbon, so why would they need to make oxidizers?
Plants make oxygen for their own use to store energy. They need this energy for cloudy days, giant flowers, and to provide an extra metabolic boost against disease outbreaks. Oxygen bubbles are useful for short term storage. But gases are unwieldy. For bulk storage the plants use the O2 to oxidize ammonia into nitrate. On Earth oxygen is a waste product that gradually built up (as organic matter was buried). But on Gasoline there is simply too little belching of oxygen and too much organic matter to oxygenate the atmosphere.
Too bad animals use their teeth and claws to rob the poor plants of their precious energy. No lungs or gills are needed! Both your fuel and oxidizer are consumed via the mouth. Predators are rare in this world: animal flesh on Earth is much easier to digest than cellulose and thus predators evolve. But on Gasoline the scarce resource is nitrate, not organic compounds. Nitrate stores in animals and plants are chemically similar, so there is much less benefit to eating animals.
Sure, why not, some reducing reactions are exothermic
Any redox reaction with a negative oxidation potential like in this chart means that it gives out usable energy when it reduces something. Ionised gold, ionised chromium, ionised group 1 metals like lithium all have such potentials.
In one iteration, your lifeforms could eat e.g. lithium, and reduce other compounds using it, resulting in oxidised lithium and reduced organics.
You then need something like plants that have an opposing reaction, that reduce lithium and maybe oxidise those same organics, with the aid of light.