…more than I had expected

I was able to talk in English better than I had expected in an online lesson on the other day.

My cat has grown up ten times as big as when I saw her for the first time.

Now we cost for food costs twice as much as before when my youngest son moved back home.

I was so impressed by the fascinating acting of the leading actress of leading part.

I saw a woman who is a balloon artist last Sunday for the first time.

I was so impressed by her work and moreover, her mind because she wants to change the world and people by making them smile using balloon art.

The bag which my mom bought yesterday was not a genuine brand.

Our car was broken down last week.

Then we asked for the garage to repair it.

At first, I heard it will be very expensive,first.

But we noticed it would be covered by the insurance, so I was very relieved.

During the online lesson I was able to talk in English better at an online lesson than I had expected on the other day.

My cat was has grown up to be ten times as big bigger as than when I had met her for the first time.

Now we cost for her food costs twice as much as it did before my youngest son moved back home.

I saw a movie the other day.

Nothing to correct :D

I was so impressed by the fascinating acting of the actress of leading part.

Technically, this is okay English, but it would be more natural to say

"I was impressed by the leading actress' fascinating performance".

I saw a woman who is balloon artist last Sunday for the first time.

Is this the first time you saw a FEMALE balloon artist? Then you should say

'I saw a female balloon artist for the first time last Sunday'

If this is the first time you saw any kind of balloon artist, you should say

'I saw for the first time a balloon artist, who is a woman, last Sunday'.

I was so impressed by her playfulness and even more by her mind that she wants her commitment to change the world and people to by making them smile by through balloon art.

I need to wipe both sides of the window of my house this weekend.

Nothing to correct :D

You can pay with these coupon tickets at the food stands here.

Nothing to correct :D

The bag which my mom bought yesterday was not genuine brand.

The last part of this sentence is not correct, but I am not sure how to fix it.

For example, if the brand you are talking about is Louis Vuitton, you might say 'was not a genuine Louis Vuitton bag'.

I was so relieved that my little brother-in-law finally got married this year.

Nothing to correct :D

Our car was broken last week.

Nothing to correct :D

Then we asked for the repair shop to repair it.

First I heard it cost that the repair was very expensive,first.

But then we noticed it would be paid by the our insurance company, so I was very relieved.

I was able to talk in English in an online lesson better than I had expected on the other day.

"In an online lesson the other day, I was able to talk in English better than I had expected." is more natural.

My cat was had grown up ten times as big as I remembered from when I had met her for the first time.My cat has grown to be ten times as big as she used to be (when I first met her).

Now we cost for the food costs twice as much as it did before my youngest son moved back home.

I was so impressed by the fascinating acting of the leading actress. of leading part.

Last Sunday, I saw a woman who is a balloon artist for the first time.

This can mean many things in English. Would you write it in Japanese?

I was so impressed by her play and even more impressed by her outlook. She wants to change the world and people to make people smile by with balloon art.

"Mind" doesn't make sense that way in English. I changed it to "outlook" - the way she sees the world.

I need to wipe both sides of the windows of at my house this weekend.

You can pay with these coupon tickets at the food stands here. or You can pay with these coupons tickets at the food stands here.

Your sentence is correct, I just made a suggestion.

The bag which my mom bought yesterday was not a genuine brand.

OR
"The bag which my mom bought yesterday was not genuine."

If you add "brand", you must say "a genuine brand".

Our car broke down last week.

When your car breaks, it "breaks down".

At first, I heard it cost would be very expensive.

But we noticed it would be paid by the insurance company, so I was very relieved.