On Saturday
(This seems like a heading or a time phrase. If it's meant to be part of a sentence, you can clarify what action is happening on Saturday.)

Because I don't have
(This is incomplete. You might mean "Because I don't have time" or "Because I don't have money," etc.)

The
(This is incomplete. A subject or noun should follow this, e.g., "The car," "The teacher," etc.)

The going to HCM City for
(This is unclear, but you might mean: "We are going to HCM City for...")

Our daughter was their classmate
(Corrected: "Our daughter was their classmate.")

The young teacher is funny and active
(Corrected: "The young teacher is funny and active.")

It's cold and windy in Hanoi
(Corrected: "It's cold and windy in Hanoi.")

We hope to see our classmates again after summer vacation
(Corrected: "We hope to see our classmates again after summer vacation.")

Our father is going to the concert in a taxi at the moment.
(Corrected: "Our father is going to the concert in a taxi at the moment.")

The shorts are $10
(Corrected: "The shorts are $10.")

Is there sugar in my coffee?
(Correct)

My brother has some new jeans.
(Correct: "some" is used for uncountable or plural nouns when we refer to an unspecified amount.)

There is an accident on the street.
(Correct: "an" is used because "accident" starts with a vowel sound.)

My dog’s hungry. Give it some bones.
(Correct: "some" is used for an unspecified quantity of countable or uncountable nouns.)

I need some paper and a pair of scissors.
(Correct: "some" is used for uncountable nouns, and "a" is used before singular countable nouns.)

There's an airport in the city.
(Correct: "an" is used before words that start with a vowel sound.)

I have a headache.
(Correct: "a" is used before singular, countable nouns.)

Are there any chocolates here?
(Correct: "any" is used in questions and negative sentences for countable nouns.)

John has a brother and an older sister.
(Correct: "a" is used for singular, countable nouns, and "an" is used before vowels.)

Would you like some coffee?
(Correct: "some" is used for an unspecified amount, especially in offers.)

I have a dog and some mice.
(Correct: "a" for singular countable nouns and "some" for plural countable nouns.)

We have to wait for 10 minutes.
(Correct: "10 minutes" indicates a specific number, no article needed.)

Is there any lemonade left?
(Correct: "any" is used in questions about uncountable nouns.)

My mother will buy 2 oranges tomorrow morning.
(Translation: "My mother will buy 2 oranges tomorrow morning.")

Do you often have a cough in winter? What season?
(Translation: "Do you often have a cough in winter? What season is your favorite?")

Mr. Smith is not standing in front of his house.
(Translation: "Mr. Smith is not standing in front of his house.")

How far is it from your house to the cinema?
(Translation: "How far is it from your house to the cinema?")

Jane is sneezing in the living room right now.
(Translation: "Jane is sneezing in the living room right now.")

Is Peter in pain these days?
(Translation: "Is Peter in pain these days?")