Grammar rules

Question 1

I am a student.

Answer 1

Yo soy (X) estudiante. 
(Because we are referring to a profession, we omit the article).

Question 2

I am a serious student.

Answer 2

Yo soy (una) estudiante seria. 
Because we specified what kind of student I am, we include the article.

Question 3

Vosotros (sois)

Answer 3

Yall

Question 4

I am Sr. Gomez.

Answer 4

Yo soy (el) Sr. Gomez. 
They are using a title to refer to themselves.

Question 5

This is professor Gomez.

Answer 5

Es (el) profesor Gomez.

You are using a title to refer to someone.

Question 6

Good day, professor Gomez.

Answer 6

Buenos dias, (X) profesor Gomez.

There is no article here because we are talking directly to the person.

Question 7

There are some books on the table.

Answer 7

Hay unos libros en la mesa.

Question 8

There is a party on Friday.

Answer 8

Hay una fiesta el viernes.

Question 9

There are three students in the class.

Answer 9

Hay tres estudientes en la clase.

Question 10

There are papers on the table.

Answer 10

Hay papeles en la mesa.

Question 11

There are some interesting people in this class.

Answer 11

Hay (unas) personas interesantes en la clase. 
We include (unas) because we are providing extra information.

Question 12

I have to go.

Answer 12

Tengo que irme.

Use tener + que when saying someone has to do something)

Question 13

I have a car.

Answer 13

Tengo (X) carro.

Take out the article unless specifying what kind of car.

Question 14

I have a Ford Fiesta car.

Answer 14

Tengo (un) carro Ford Fiesta.

We include the article because we are specifying what kind of car.