I was thinking about a source of power for one of my civilizations. Chemical power, specifically giant batteries, have always been A cool idea to me. I want to know how realistic this is. I want it/them to be able to power at least a village or small town.
I think you are talking about fuel cells rather than what we generally think of as batteries. That is, you need to take some chemicals and react them together, producing electricity as a byproduct. But the (non-rechargable) battery is a single-use device. For instance, the common alkaline battery works by reacting zinc & manganese dioxide: https://en.wikipedia.org/wiki/Alkaline_battery The battery is a fairly complex structure manufactured to do that, which produces a relatively small amount of power, and which you throw away when the reactants are used up.
A fuel cell (sometimes called a "flow battery": https://en.wikipedia.org/wiki/Flow_battery ) is a device that combines reactants from outside. For instance, perhaps the commonest fuel cell (as used in spacecraft &c) reacts hydrogen & oxygen to produce water, and it can keep on doing so as long as you keep providing it with H2 & O2. (In theory: of course like anything else, it'll eventually wear out.)
So if your civilization happens to be really good chemists, they could develop fuel cells that run on common substances. For instance, Earthly researchers have developed fuel cells that run on sugar or alcohol: https://en.wikipedia.org/wiki/Direct-ethanol_fuel_cell There are also ones that run on methane, so it's certainly conceiveable to have one running on petroleum or natural gas.
Bottom line: non-rechargeable batteries, no. (Rechargeables aren't a power source, but are useful for e.g. load smoothing in a power grid, as mentioned in comments.) You'd soon have a giant worn-out battery dump. But fuel cells are workable.
It would be possible, but hugely impractical
Yes, it is possible to power up everything from non-rechargeable batteries. But you will need a lot of those batteries.
Let's consider an example. Say, a village has 100 households, and each consumes 20 kWh a day on average. This gives us 2,000 kWh for the everyone in the village (private consumers). Let's say that village's businesses consume just as much, which gives us 4,000 kWh a day total.
Now let's take a look at the energy density of batteries: Comparison of commercial battery types. Historically popular zinc-carbon batteries can hold 36 Wh/kg, while modern alkaline can hold 85–190 Wh/kg. The most efficient kind seems to be Lithium-carbon monofluoride, which can hold up to 780 Wh/kg.
Converting it to the village energy daily needs, we are getting 111 tons of zinc-carbon batteries, at least 21 tons of alkalines, or at least 5 tons of the most fancy lithium batteries. Every day.
Thus, a modest village would need a big factory to cover its need for battery power.
A large enough battery could easily be built to supply power to a village or even a small town for a few days. Perhaps even a week or two. It really is just a matter of scale. If you want twice the capacity then double the number of battery cells in your battery.
It would obviously depend on the technology level, but it would be possible with modern technology or even late 19th century technology. The real question is why on earth would you want to do that? As soon as the battery was flat there would be no power. If the intention was then to recharge it from an available energy source, why not just connect to the energy source directly.
If the reason is that the energy source is intermittent then there are much better ways to store large amounts of energy than conventional batteries such as pumped water or even a cryobattery . https://highviewpower.com/technology/
If you have somewhere with a giant lake or aquifer of naturally occuring sulfuric acid, and a rich source of lead and lead oxides, then there is a lot of potential energy to be unlocked in turning that acid lake into a giant lead-acid battery. So you basically treat your lake like a massive, single use, car battery.
For difficulty to make: It is very easy to make, but not necessarily cheap. Lead is a very easy metal to refine and work with due to its low melting temperature and high malleability, and the system itself is as simple as putting two metal bars into your acid lake. The problem is that the lead bars will be spent pretty quickly and need to be replaced. Refining the lead may lead to a net power loss in which case you are looking at a pretty impractical system.
For Size: you will consume a volume of lead and acid about equal to 13 car batteries a day for an average household. For comparison, you need to burn 2.75 gallons of oil a day to power a house; so, it is going to be several times less size efficient as far as fuel goes, but require a much more simple powerplant.
For Waste: Your waste products will be water and lead sulfate. Disposing of waste water is not a big deal, but you will go through a lot of lead which is both heavy and toxic... so probably not easy to safely dispose of.
If you are looking to pair this system with a renewable resource, lead-acid batteris are rechargeable; so, if you tie a solar grid into your lead-acid battery lake, then there is no real waste, and your battery could easilly store enough portential energy to get you through long dark periods.
