1. What do you want to be in the future?

- I want to be a certified real estate agent.

2. What do you want to become in the future?
-I want to become a certified real estate agent.

3. What do your parents want you to become?
- They want me to become a public prosecutor.

4. What do your parents want you to be?
- They want me to be a public prosecutor.

(Are the questions and answers all grammatical? Can we use both 'be' and 'become'? Which one is commonly used, 'be' or 'become'?)

Both are equivalent. Like the examples, which you use in the answer would probably depend on how the question is phrased.

Yes, all the questions and answers are grammatically correct. Both "be" and "become" are commonly used when discussing future goals or career aspirations. However, there is a subtle difference in meaning between the two.

- "Be" is used to describe a state of being or identity. For example, "I want to be a real estate agent" suggests that you want to exist in the state of being a real estate agent. It implies that you already identify with that profession.

- "Become" is used to describe a process or change. For example, "I want to become a real estate agent" implies that you currently are not a real estate agent, but you desire to go through a process or achieve a goal to transform into one.

In the context of future goals and aspirations, both "be" and "become" are commonly used. It ultimately depends on the personal preference and style of the speaker.