Nell want to get a pet.
Pay attention to the tense which is simple past tense.
Nell wanted to get a pet.

She and her dad went to a pet shop.
Ok!

Every pet have there good thing and bad thing.
Simple past tense!
{There}?! Don’t understand.
{Thing} should be in plural form.
Every pet had good things and bad things.

Her dad and she see the pats. “No, Nell not a pup.”
Simple past tense!
You mean {pets}?
Her dad and she saw the pets. “No, Nell. Not a pup.”

Dad don’t let Nell to have a pup and other.
Simple past tense! Also change {and} into {or} in a negative sentence.
{Other} is an adj. {Others} is a pronoun.
Dad didn’t let Nell to have a pup or others.

Her dad want a bat but it is to expensive.
Simple past tense!
Also pay attention to your spelling.
Her dad wanted a bat but it was too expensive.