Many foods

Persian LearnerIs the above sentence grammatical and natural?

No. You are misusing 'foods'.

I have eaten many meals here and they were not good.

I have eaten a lot of food here and it is not good.

What about the following one?

I have eaten many types of foods and they were not good.

You know, Mister Micawber, my friend goes to an English school. She is at the elementary level. Today she managed to take a picture of the board. I noticed the given sentence and it seemed bad English to me. So, I put it here to make sure.

One of the sentences on the paper is I have cut my hair.

This sentence is wrong. How can you cut your hair?

tamguatlayThis sentence is wrong. How can you cut your hair?

You are right. It doesn't make sense. It should have been " I've had my hair cut."

The teacher wanted to make some sentences to teach the perfect aspect; he hasn't cared much about the naturalness of the sentences.

The teacher wanted to make some sentences to teach the perfect aspect; he hasn't cared much about the naturalness of the sentences. (I don't think so. "I cut my hair" is one of the commonest mistakes made by non-native teachers and speakers. I think your teacher doesn't know that the sentence is wrong. You could ask her whether she thinks the sentence is incorrect.)

tamguatlay I have cut my hair.

That is perfectly natural and common. It means 'I have had my hair cut'.

Persian LearnerI have eaten many types of foods and they were not good.

That is a better use of 'foods'. The student's version would not be wrong in appropriate context.

Mister Micawber The student's version would not be wrong in appropriate context.

May I ask you to give an example, sir?

Persian LearnerMay I ask you to give an example, sir?

In a discussion in a Nutrition seminar.