People in the village relisubsisted on farming for a living and had little money.

This sentence is grammatically correct as is. But this sounds a bit more natural.

To get a sow pregnant, we needed to take ither to a nearby town to breed with a boar and then bring ither back home.

Nothing wrong with using "it" for an animal, but you do refer to the sow as a "her" later.

When a sow was about to give birth, we needed to care for her very carefullye had to tend to a sow carefully when it was about time for one to give birth.

Nothing wrong with your original sentence! But there's a repeating pattern of "dependent clause, main clause" throughout the paragraph so far that would be good to break. Plus it sounds nicer when you don't repeat things like "we needed to."

WhenOnce she began giving birth, it happened quickly, but she needed to rest briefly between each piglet.

"Once" at the start of a clause has a more specific, sequential connotation vs "where."

When the pigletsy reached a certain age, we had the male piglets castrated to help them grow faster and stronger.

Fine to use a pronoun here as you're alredy specifying who "they" are later in the sentence. Could swap to:

When the male piglets reached a certain age, we had them...
or
When they reached a certain age, we had the males...

In the countryside, some people madke a living by castrating male piglets.

Do people still make a living this way? Might be clearer to highlight when people made a living this way if you're going to use "made."

Back then, some people made...

Before they were taken to market, they were healthy, strong, and their coats were shiny, makinghad shiny coats that made them look very beautiful.

This is a comma splice. My suggestion is to rewrite the sentence a bit to specify that their shiny coats were the reason they looked beautiful.

Removing "very" as it weakens the sentence. Overuse of words like "very" or "really" is common among native speakers, but it's considered a bad habit and not good writing.

When I was a child living in a small village, our living conditions were very poorsqualid.

To get a sow pregnant, we needed to take it to a nearby town to breed it with a boar and then bring it back home.

We had to determine when she would give birth and then stay with her throughout the entire birthing processr pregnancy.

I still remember one night when we hung a barn lantern in the sty while waiting for her to give birth.

听起来耶稣的出生故事

When she began giving birth, it happened quickly, but she needed to rest briefly between each piglet.

We couldn’t leave even after she finished giving birth because we still needed to care for the newborn piglets; otherwise, they might be accidentally crushed by their mother, as the sow was too exhausted to noticepay attention.

Although my family raised several sows, it didn’t significantly improve our financial situation significantly.

in some contexts, adverbs are placed at the end

From what I overheard in my parents’ conversations, we were still short of moneypoor.

or broke (same as poor) in informal english