1. What’s there for our breakfast?
a. there is bread and eggs. b. There is eggs and bread.
c. There is noodles and chicken d. There are chicken and noodles.
I choose: “a”

2. what is your favorite food?
a. My favorite food is the apple. b. My favorite food is an apple.
c. My favorite is apple. d. My favorite food is the apples.

I choose : d. My favorite food is the apples.

1. What do you like for dinner?
a. I like fish b. I like a fish
c. I like the fish d. I like fishes

I choose: a. I like fish

1. Who has a round face? Your brother or her brother?
a. Yes, my brother has a round face b. No, my brother has not a round face.
c. My brother has a round face.

I choose c. My brother has a round face.

1. I am delighted that you pass/ passed your exam.

If you’ve taken this from a book which includes a question, “What’s there for our breakfast?” I wouldn’t rate the book too highly.

What is there for breakfast? would be passable, but not with an apostrophe -s
If you want to use the apostrophe then:
What’s for breakfast?

Possibly the answers the book gives will be no more correct than the questions are.

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1. What is there for our breakfast?
a. There is bread and eggs. b. There is eggs and bread.
c. There is noodles and chicken d. There are chicken and noodles.
I choose: “a”

a, b and c are all possible answers, though not necessarily what you might like for breakfast. ‘bread and eggs’ is less likely than ‘eggs and bread’ because the protein food is usually mentioned first.
As the question is ‘what is…’ then the answer should be 'there is…

1. what is your favorite food?
a. My favorite food is the apple. b. My favorite food is an apple.
c. My favorite is apple. d. My favorite food is the apples.

I choose : d. My favorite food is the apples.
The answer is c. In this context we are not looking at the individual fruit.

1. What do you like for dinner?
a. I like fish b. I like a fish
c. I like the fish d. I like fishes

I choose: a. I like fish

• You are correct for the same reason as given in the previous question.
1. Who has a round face? Your brother or her brother?
a. Yes, my brother has a round face b. No, my brother has not a round face.
c. My brother has a round face.

I choose c. My brother has a round face.
You are correct.

1. I am delighted that you pass/ passed your exam.

passed - the event has already happened even though the speaker is delighted now.
“I was delighted that…” is also possible.

[color=green]Possibly the answers the book gives will be no more correct than the questions are.

1. What is there for our breakfast?
a. There is bread and eggs. b. There is eggs and bread.
c. There is noodles and chicken d. There are chicken and noodles.
I choose: “a”
[color=green]
a, b and c are all possible answers, though not necessarily what you might like for breakfast. ‘bread and eggs’ is less likely than ‘eggs and bread’ because the protein food is usually mentioned first. In the same way ‘chicken and noodles’ would be more likely than ‘noodles and chicken’, but in this case ‘noodles and chicken’ cannot be right because the sentence uses ‘are’.
As the question is ‘what is…’ then the answer should be 'there is…

2. what is your favorite food?
a. My favorite food is the apple. b. My favorite food is an apple.
c. My favorite is apple. d. My favorite food is the apples.

I choose : d. My favorite food is the apples.
[color=green]The answer is c. In this context we are not looking at the individual fruit.

1. What do you like for dinner?
a. I like fish b. I like a fish
c. I like the fish d. I like fishes

I choose: a. I like fish
[color=green] - You are correct for the same reason as given in the previous question.

1. Who has a round face? Your brother or her brother?
a. Yes, my brother has a round face b. No, my brother has not a round face.
c. My brother has a round face.

I choose c. My brother has a round face.
[color=green]You are correct.

1. I am delighted that you pass/ passed your exam.

[color=green]passed - the event has already happened even though the speaker is delighted now.
“I was delighted that…” is also possible.