1. I feel like a princess.

2. I feel like a millionaire.
3. I feel like a cup of coffee.
4. I feel like going to a movie.
5. I feel like I am a millionaire.
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Are they all grammatical?

Yes, they are grammatical.

To check if these sentences are grammatically correct, we need to analyze the structure and usage of the phrases “feel like” and the comparisons being made.

1. "I feel like a princess."
This sentence is grammatically correct. It is using a simile to compare the speaker's emotional state to that of a princess.

2. "I feel like a millionaire."
This sentence is also grammatically correct. It uses a simile to compare the speaker's emotional state to that of a millionaire.

3. "I feel like a cup of coffee."
This sentence is grammatically correct as well. It uses a simile to compare the speaker's emotional state to that of a cup of coffee, implying that the speaker has a desire or need for coffee.

4. "I feel like going to a movie."
This sentence is grammatically correct. It uses the phrase "feel like" to indicate a desire or inclination, followed by the gerund "going" to indicate the desired action of going to a movie.

5. "I feel like I am a millionaire."
This sentence is also grammatically correct. It uses the phrase "feel like" to express an emotional state, followed by the comparison "I am a millionaire" to emphasize the intensity or intensity of the feeling.

In summary, all the sentences are grammatically correct as they use appropriate structures to convey the desired meanings.