with usage

[navi tasan]

Which are correct:

1-The animal died with a lot of pain.
2-The animal was killed with a lot of pain.
3-They killed the animal with a lot of pain.

I think "1" is correct but "2" and "3" might seem to be saying that "pain" was used to kill the animal. I am not sure about them.

Maybe this is better:

4-They killed the animal painfully.

[Raymott]

Which are correct:

1-The animal died with a lot of pain.
2-The animal was killed with a lot of pain.
3-They killed the animal with a lot of pain.

I think "1" is correct but "2" and "3" might seem to be saying that "pain" was used to kill the animal. I am not sure about them.

Maybe this is better:

4-They killed the animal painfully.

Do you mean that the animal suffered a lot pain while it died, or the killers felt pain? All of your sentences could mean either. None of them are good.
I'll assume you mean the animal was in pain.

You can say:
The animal died in a lot of pain.
The animal suffered a lot [of pain] in dying.
They caused the animal a lot of pain in killing it.
They made the animal suffer as they killed it.
Killing the animal caused it a lot of pain.
Klling the animal caused it to suffer as it died.
...