An old rancher quotetold this story:

As someone else said, usually you wouldn't say "quoted a story". It would likely be "told".

A female wolf had given birth to a few pups in a small stall in our sheep pen.

We waited to see what would happen; w. When she came back and saw the scene, she attacked her pups; she was beating and bitting them and the pups kept screaming.

I would not use two semicolons in the same sentence like that. Try to only use it once, for the two clauses that are most linked. Also, biting was misspelled.

This is a wolf known for its fierce, wild, and brutal nature, but it understands that when it enters someone's life, gets sheltered and is shown kindness, it shouldn't betray them, and should compaensate them for theany harm done to them.

I don't think this is actually grammatically incorrect, but it is a very long sentence which should probably be avoided.

You also don't need to repeat the "is" at "is shown kindness". You could say "gets sheltered and gets shown kindness" which can simply be reduced to "gets sheltered and shown kindness" or something similar.

You also don't need to say "them" after compensate.

It is also maybe more common to say "harm caused" but "harm done" also sounds okay.

I'd also probably specify that the harm was caused by the wolf or its young specifically and is not just any harm done to the person.

It is also more common to say "any harm" as this suggests you should compensate for anything bad you do to the person, whereas "the harm" suggests that you are always going to cause harm by being sheltered by someone which isn't necessarily true.

Also, misspelling of "compensate".

Perhaps:
"This is a wolf known for its fierce, wild and brutal nature. However, it understands that when it enters someone's life, is sheltered and shown kindness, it shouldn't betray them and should compensate for any harm it causes."

Every essense is amendable, but the corrupt nature!

I'm not really sure what this sentence is supposed to mean? It seems like it was supposed to be a nice dramatic end but I think it needed a bit more information to actually understand it.
So I can't really comment much on this, but I will ask if you maybe meant to use "commendable" instead of "amendable"?

An old rancher quoted this story:

What you wrote is not incorrect, but, we would usually say "An old rancher told this story"

A female wolf had given birth to a few pups in a small stall in our sheep pen.

She would go hunting, and every time she would catcreturn with a chicken, a rabbit, or a lamb and brshe had caught, bringing it for her pups.

What you wrote is not wrong but is confusing to read because "every time she would catch..." sounds like it is going to introduce a dependent clause, but in this case it is not. To make it easier to read, I reworded it.

Even though she‌ kept going back and forth tohrough the sheep pen, she would never disturb the sheep.

I think she is going through and beyond the sheep pen, not just to it (which implies that it is her destination)

We waited to see what would happen; when she came back and saw the scene, she attacked her pups; she was beahitting and bitting them and the pups kept screaming.

"Beating" sounds like an action taken by a humanoid--striking with their hands.

The next day, and to our great surprise, we saw that she had caught a lamb, which was still aliveithout killing it.

Your story sounds like you actually saw her catch the lamb, and then saw her drop it down the pen.

If that is what you mean, then it's fine.

But if you mean that you saw the lamb that she had left in the stall, and inferred that she had done this, then I would like to suggest:

The next day, to our great surprise, we discovered that she had caught a lamb without killing it, and had dropped it down the wall into our pen.

She had dropped it down the pen's wall and left.

See previous comment. The story as written implies you (the reader) actually watched the wolf drop the lamb.

This is a wolfn animal known for its fierce, wild, and brutal nature, but it understands that when it enters someone's life, gets sheltered and is shown kindness, it shouldn't betray them, and should compaensate them for theany harm done to them.

As written this means that this particular wolf is known for its wild nature.

I speculate that you mean that this species is known for this, so I adjusted it to not mean this wolf in particular.

Every essense is amendable, but the corrupt nature!

I'm afraid that I don't understand what this means.